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InternLM 238

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.subst_idem

[101, 9]

[116, 21]

rw [Nat.add_assoc]

case mp.semiR P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ Nat.succ 0 < 1 + sizeOf l✝ + sizeOf r✝

case mp.semiR P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ Nat.succ 0 < 1 + (sizeOf l✝ + sizeOf r✝)

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.subst_idem

[101, 9]

[116, 21]

apply Nat.lt_add_of_pos_right

case mp.semiR P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ Nat.succ 0 < 1 + (sizeOf l✝ + sizeOf r✝)

case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝ + sizeOf r✝

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.subst_idem

[101, 9]

[116, 21]

first | (apply Nat.add_pos_left; apply sizeOf_pos) | (apply Nat.add_pos_right; apply sizeOf_pos)

case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝ + sizeOf r✝

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.subst_idem

[101, 9]

[116, 21]

(apply Nat.add_pos_left; apply sizeOf_pos)

case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝ + sizeOf r✝

case mp.semiR.h.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.subst_idem

[101, 9]

[116, 21]

apply Nat.add_pos_left

case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝ + sizeOf r✝

case mp.semiR.h.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.subst_idem

[101, 9]

[116, 21]

apply sizeOf_pos

case mp.semiL.h.h P✝ : Sort u_1 b : Bunch P✝ l✝ : BunchWithHole P✝ r✝ : Bunch P✝ h : (subst b l✝ ;ᵇ r✝) = b ⊢ 0 < sizeOf l✝

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.subst_idem

[101, 9]

[116, 21]

(apply Nat.add_pos_right; apply sizeOf_pos)

case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝ + sizeOf r✝

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.subst_idem

[101, 9]

[116, 21]

apply Nat.add_pos_right

case mp.semiR.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf l✝ + sizeOf r✝

case mp.semiR.h.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf r✝

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.subst_idem

[101, 9]

[116, 21]

apply sizeOf_pos

case mp.semiR.h.h P✝ : Sort u_1 b l✝ : Bunch P✝ r✝ : BunchWithHole P✝ h : (l✝ ;ᵇ subst b r✝) = b ⊢ 0 < sizeOf r✝

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.subst_idem

[101, 9]

[116, 21]

rintro rfl

case mpr P✝ : Sort u_1 b : Bunch P✝ Γ : BunchWithHole P✝ ⊢ Γ = hole → subst b Γ = b

case mpr P✝ : Sort u_1 b : Bunch P✝ ⊢ subst b hole = b

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.subst_idem

[101, 9]

[116, 21]

simp

case mpr P✝ : Sort u_1 b : Bunch P✝ ⊢ subst b hole = b

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.idem_subst

[118, 9]

[120, 7]

rw [eq_comm]

P✝ : Sort u_1 b : Bunch P✝ Γ : BunchWithHole P✝ ⊢ b = subst b Γ ↔ Γ = hole

P✝ : Sort u_1 b : Bunch P✝ Γ : BunchWithHole P✝ ⊢ subst b Γ = b ↔ Γ = hole

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.idem_subst

[118, 9]

[120, 7]

simp

P✝ : Sort u_1 b : Bunch P✝ Γ : BunchWithHole P✝ ⊢ subst b Γ = b ↔ Γ = hole

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.comp_hole

[148, 9]

[149, 30]

induction Γ <;> simp_all

P : Sort u_1 Γ : BunchWithHole P ⊢ Γ.comp hole = Γ

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.comp_def

[151, 1]

[153, 55]

induction h1 <;> simp_all [comp, FunLike.coe, subst]

P : Sort u_1 h1 h2 : BunchWithHole P b : Bunch P ⊢ ↑(h1.comp h2) b = ↑h1 (↑h2 b)

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_prop

[155, 9]

[157, 40]

cases Γ <;> simp [FunLike.coe, subst]

P : Sort u_1 b : Bunch P φ : Typ P Γ : BunchWithHole P ⊢ ↑Γ b = prop φ ↔ Γ = hole ∧ b = prop φ

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.prop_eq

[159, 9]

[162, 7]

rw [show (prop φ = _ ↔ _ = prop φ) from ⟨Eq.symm, Eq.symm⟩]

P : Sort u_1 φ : Typ P b : Bunch P Γ : BunchWithHole P ⊢ prop φ = ↑Γ b ↔ Γ = hole ∧ b = prop φ

P : Sort u_1 φ : Typ P b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = prop φ ↔ Γ = hole ∧ b = prop φ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.prop_eq

[159, 9]

[162, 7]

simp

P : Sort u_1 φ : Typ P b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = prop φ ↔ Γ = hole ∧ b = prop φ

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_cunit

[164, 9]

[166, 40]

cases Γ <;> simp [FunLike.coe, subst]

P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = cunit ↔ Γ = hole ∧ b = cunit

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.cunit_eq

[168, 9]

[171, 7]

rw [show (_ = _ ↔ _ = _) from ⟨Eq.symm, Eq.symm⟩]

P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ cunit = ↑Γ b ↔ Γ = hole ∧ b = cunit

P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = cunit ↔ Γ = hole ∧ b = cunit

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.cunit_eq

[168, 9]

[171, 7]

simp

P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = cunit ↔ Γ = hole ∧ b = cunit

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_sunit

[173, 9]

[175, 40]

cases Γ <;> simp [FunLike.coe, subst]

P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = sunit ↔ Γ = hole ∧ b = sunit

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.sunit_eq

[177, 9]

[180, 7]

rw [show (_ = _ ↔ _ = _) from ⟨Eq.symm, Eq.symm⟩]

P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ sunit = ↑Γ b ↔ Γ = hole ∧ b = sunit

P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = sunit ↔ Γ = hole ∧ b = sunit

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.sunit_eq

[177, 9]

[180, 7]

simp

P : Sort u_1 b : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = sunit ↔ Γ = hole ∧ b = sunit

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_comma

[182, 1]

[188, 20]

cases Γ <;> aesop

P : Sort u_1 b Δ₁ Δ₂ : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = (Δ₁ ,ᵇ Δ₂) ↔ Γ = hole ∧ b = (Δ₁ ,ᵇ Δ₂) ∨ (∃ Γ', Γ = commaL Γ' Δ₂ ∧ ↑Γ' b = Δ₁) ∨ ∃ Γ', Γ = commaR Δ₁ Γ' ∧ ↑Γ' b = Δ₂

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_semi

[190, 1]

[196, 20]

cases Γ <;> aesop

P : Sort u_1 b Δ₁ Δ₂ : Bunch P Γ : BunchWithHole P ⊢ ↑Γ b = (Δ₁ ;ᵇ Δ₂) ↔ Γ = hole ∧ b = (Δ₁ ;ᵇ Δ₂) ∨ (∃ Γ', Γ = semiL Γ' Δ₂ ∧ ↑Γ' b = Δ₁) ∨ ∃ Γ', Γ = semiR Δ₁ Γ' ∧ ↑Γ' b = Δ₂

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

intro h

P : Sort u_1 Γ Γ' : BunchWithHole P φ φ' : Bunch P ⊢ ↑Γ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ Γ.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = Γ) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = Γ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

P : Sort u_1 Γ Γ' : BunchWithHole P φ φ' : Bunch P h : ↑Γ φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ Γ.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = Γ) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = Γ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

induction Γ generalizing Γ'

P : Sort u_1 Γ Γ' : BunchWithHole P φ φ' : Bunch P h : ↑Γ φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ Γ.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = Γ) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = Γ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

case hole P : Sort u_1 φ φ' : Bunch P Γ' : BunchWithHole P h : ↑hole φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ hole.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = hole) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = hole ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ case commaL P : Sort u_1 φ φ' : Bunch P l✝ : BunchWithHole P r✝ : Bunch P l_ih✝ : ∀ {Γ' : BunchWithHole P}, ↑l✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ l✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = l✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = l✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑(commaL l✝ r✝) φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (commaL l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = commaL l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = commaL l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ case commaR P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P r_ih✝ : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑(commaR l✝ r✝) φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (commaR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = commaR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = commaR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ case semiL P : Sort u_1 φ φ' : Bunch P l✝ : BunchWithHole P r✝ : Bunch P l_ih✝ : ∀ {Γ' : BunchWithHole P}, ↑l✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ l✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = l✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = l✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑(semiL l✝ r✝) φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiL l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiL l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiL l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ case semiR P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P r_ih✝ : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑(semiR l✝ r✝) φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

case hole => simp_all

P : Sort u_1 φ φ' : Bunch P Γ' : BunchWithHole P h : ↑hole φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ hole.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = hole) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = hole ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

simp_all

P : Sort u_1 φ φ' : Bunch P Γ' : BunchWithHole P h : ↑hole φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ hole.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = hole) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = hole ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

simp at h

P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑(semiR l✝ r✝) φ = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : (l✝ ;ᵇ ↑r✝ φ) = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

rw [eq_comm] at h

P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : (l✝ ;ᵇ ↑r✝ φ) = ↑Γ' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑Γ' φ' = (l✝ ;ᵇ ↑r✝ φ) ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

first | rw [eq_comma] at h | rw [eq_semi] at h

P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑Γ' φ' = (l✝ ;ᵇ ↑r✝ φ) ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : Γ' = hole ∧ φ' = (l✝ ;ᵇ ↑r✝ φ) ∨ (∃ Γ'_1, Γ' = semiL Γ'_1 (↑r✝ φ) ∧ ↑Γ'_1 φ' = l✝) ∨ ∃ Γ'_1, Γ' = semiR l✝ Γ'_1 ∧ ↑Γ'_1 φ' = ↑r✝ φ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

rcases h with (⟨rfl,rfl⟩|⟨Γ'',rfl,h⟩|⟨Γ'',rfl,h⟩)

P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : Γ' = hole ∧ φ' = (l✝ ;ᵇ ↑r✝ φ) ∨ (∃ Γ'_1, Γ' = semiL Γ'_1 (↑r✝ φ) ∧ ↑Γ'_1 φ' = l✝) ∨ ∃ Γ'_1, Γ' = semiR l✝ Γ'_1 ∧ ↑Γ'_1 φ' = ↑r✝ φ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

case inl.intro P : Sort u_1 φ l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' (l✝ ;ᵇ ↑r✝ φ) → (∃ Δ, φ = ↑Δ (l✝ ;ᵇ ↑r✝ φ) ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, (l✝ ;ᵇ ↑r✝ φ) = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' (l✝ ;ᵇ ↑r✝ φ) = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ (∃ Δ, φ = ↑Δ (l✝ ;ᵇ ↑r✝ φ) ∧ (semiR l✝ r✝).comp Δ = hole) ∨ (∃ Δ, (l✝ ;ᵇ ↑r✝ φ) = ↑Δ φ ∧ hole.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = hole ∧ Δ' (l✝ ;ᵇ ↑r✝ φ) = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ case inr.inl.intro.intro P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑Γ'' φ' = l✝ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = semiL Γ'' (↑r✝ φ)) ∨ (∃ Δ, φ' = ↑Δ φ ∧ (semiL Γ'' (↑r✝ φ)).comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = semiL Γ'' (↑r✝ φ) ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ case inr.inr.intro.intro P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑Γ'' φ' = ↑r✝ φ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = semiR l✝ Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ (semiR l✝ Γ'').comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = semiR l✝ Γ'' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

rw [eq_comma] at h

P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑Γ' φ' = (l✝ ,ᵇ ↑r✝ φ) ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (commaR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = commaR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = commaR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : Γ' = hole ∧ φ' = (l✝ ,ᵇ ↑r✝ φ) ∨ (∃ Γ'_1, Γ' = commaL Γ'_1 (↑r✝ φ) ∧ ↑Γ'_1 φ' = l✝) ∨ ∃ Γ'_1, Γ' = commaR l✝ Γ'_1 ∧ ↑Γ'_1 φ' = ↑r✝ φ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (commaR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = commaR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = commaR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

rw [eq_semi] at h

P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : ↑Γ' φ' = (l✝ ;ᵇ ↑r✝ φ) ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ' : BunchWithHole P h : Γ' = hole ∧ φ' = (l✝ ;ᵇ ↑r✝ φ) ∨ (∃ Γ'_1, Γ' = semiL Γ'_1 (↑r✝ φ) ∧ ↑Γ'_1 φ' = l✝) ∨ ∃ Γ'_1, Γ' = semiR l✝ Γ'_1 ∧ ↑Γ'_1 φ' = ↑r✝ φ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

simp

case inl.intro P : Sort u_1 φ l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' (l✝ ;ᵇ ↑r✝ φ) → (∃ Δ, φ = ↑Δ (l✝ ;ᵇ ↑r✝ φ) ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, (l✝ ;ᵇ ↑r✝ φ) = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' (l✝ ;ᵇ ↑r✝ φ) = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ (∃ Δ, φ = ↑Δ (l✝ ;ᵇ ↑r✝ φ) ∧ (semiR l✝ r✝).comp Δ = hole) ∨ (∃ Δ, (l✝ ;ᵇ ↑r✝ φ) = ↑Δ φ ∧ hole.comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = hole ∧ Δ' (l✝ ;ᵇ ↑r✝ φ) = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

simp

P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑Γ'' φ' = ↑r✝ φ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = semiR l✝ Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ (semiR l✝ Γ'').comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = semiR l✝ Γ'' ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑Γ'' φ' = ↑r✝ φ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

rw [eq_comm] at h

P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑Γ'' φ' = ↑r✝ φ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ

P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑r✝ φ = ↑Γ'' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

rcases ih h with (h1|h2|⟨Δ,Δ',rfl,rfl,h3⟩) <;> clear ih h

P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑r✝ φ = ↑Γ'' φ' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ

case inl P : Sort u_1 φ φ' l✝ : Bunch P r✝ Γ'' : BunchWithHole P h1 : ∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ case inr.inl P : Sort u_1 φ φ' l✝ : Bunch P r✝ Γ'' : BunchWithHole P h2 : ∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ case inr.inr.intro.intro.intro.intro P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ (∃ Δ_1, φ = ↑Δ_1 φ' ∧ (Δ' φ').comp Δ_1 = Δ φ) ∨ (∃ Δ_1, φ' = ↑Δ_1 φ ∧ (Δ φ).comp Δ_1 = Δ' φ') ∨ ∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

simp [h1]

case inl P : Sort u_1 φ φ' l✝ : Bunch P r✝ Γ'' : BunchWithHole P h1 : ∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'' ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

simp [h2]

case inr.inl P : Sort u_1 φ φ' l✝ : Bunch P r✝ Γ'' : BunchWithHole P h2 : ∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ'') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ''.comp Δ = r✝) ∨ ∃ Δ, Δ φ = semiR l✝ Γ'' ∧ ∃ x, x φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

apply Or.inr

case inr.inr.intro.intro.intro.intro P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ (∃ Δ_1, φ = ↑Δ_1 φ' ∧ (Δ' φ').comp Δ_1 = Δ φ) ∨ (∃ Δ_1, φ' = ↑Δ_1 φ ∧ (Δ φ).comp Δ_1 = Δ' φ') ∨ ∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ

case inr.inr.intro.intro.intro.intro.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ (∃ Δ_1, φ' = ↑Δ_1 φ ∧ (Δ φ).comp Δ_1 = Δ' φ') ∨ ∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

apply Or.inr

case inr.inr.intro.intro.intro.intro.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ (∃ Δ_1, φ' = ↑Δ_1 φ ∧ (Δ φ).comp Δ_1 = Δ' φ') ∨ ∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ

case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

iterate 2 ( first | refine ⟨(fun x => commaL _ _),rfl,?_⟩ | refine ⟨(fun x => commaR _ _),rfl,?_⟩ | refine ⟨(fun x => semiL _ _),rfl,?_⟩ | refine ⟨(fun x => semiR _ _),rfl,?_⟩ )

case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ Δ_1, Δ_1 φ = semiR l✝ (Δ φ) ∧ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ_1 ψ) ψ' = ↑(x ψ') ψ

case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

intro ψ ψ'

case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ

case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ψ ψ' : Bunch P ⊢ ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

simp [h3]

case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ψ ψ' : Bunch P ⊢ ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

( first | refine ⟨(fun x => commaL _ _),rfl,?_⟩ | refine ⟨(fun x => commaR _ _),rfl,?_⟩ | refine ⟨(fun x => semiL _ _),rfl,?_⟩ | refine ⟨(fun x => semiR _ _),rfl,?_⟩ )

case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑(x ψ') ψ

case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

first | refine ⟨(fun x => commaL _ _),rfl,?_⟩ | refine ⟨(fun x => commaR _ _),rfl,?_⟩ | refine ⟨(fun x => semiL _ _),rfl,?_⟩ | refine ⟨(fun x => semiR _ _),rfl,?_⟩

case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑(x ψ') ψ

case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

refine ⟨(fun x => commaL _ _),rfl,?_⟩

case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' r✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ x, x φ' = commaL (Δ' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaL (Δ x) r✝) ψ) ψ' = ↑(x ψ') ψ

case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' r✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaL (Δ x) r✝) ψ) ψ' = ↑((fun x => commaL (Δ' x) r✝) ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

refine ⟨(fun x => commaR _ _),rfl,?_⟩

case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ x, x φ' = commaR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaR l✝ (Δ x)) ψ) ψ' = ↑(x ψ') ψ

case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaR l✝ (Δ x)) ψ) ψ' = ↑((fun x => commaR l✝ (Δ' x)) ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

refine ⟨(fun x => semiL _ _),rfl,?_⟩

case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' r✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ x, x φ' = semiL (Δ' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL (Δ x) r✝) ψ) ψ' = ↑(x ψ') ψ

case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' r✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL (Δ x) r✝) ψ) ψ' = ↑((fun x => semiL (Δ' x) r✝) ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

refine ⟨(fun x => semiR _ _),rfl,?_⟩

case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∃ x, x φ' = semiR l✝ (Δ' φ') ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑(x ψ') ψ

case inr.inr.intro.intro.intro.intro.h.h P : Sort u_1 φ φ' l✝ : Bunch P Δ Δ' : Bunch P → BunchWithHole P h3 : ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiR l✝ (Δ x)) ψ) ψ' = ↑((fun x => semiR l✝ (Δ' x)) ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

cases h

P : Sort u_1 φ φ' l✝ : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P h : ↑Γ'' φ' = l✝ ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR l✝ r✝).comp Δ = semiL Γ'' (↑r✝ φ)) ∨ (∃ Δ, φ' = ↑Δ φ ∧ (semiL Γ'' (↑r✝ φ)).comp Δ = semiR l✝ r✝) ∨ ∃ Δ Δ', Δ φ = semiL Γ'' (↑r✝ φ) ∧ Δ' φ' = semiR l✝ r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR (↑Γ'' φ') r✝).comp Δ = semiL Γ'' (↑r✝ φ)) ∨ (∃ Δ, φ' = ↑Δ φ ∧ (semiL Γ'' (↑r✝ φ)).comp Δ = semiR (↑Γ'' φ') r✝) ∨ ∃ Δ Δ', Δ φ = semiL Γ'' (↑r✝ φ) ∧ Δ' φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

simp

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ (∃ Δ, φ = ↑Δ φ' ∧ (semiR (↑Γ'' φ') r✝).comp Δ = semiL Γ'' (↑r✝ φ)) ∨ (∃ Δ, φ' = ↑Δ φ ∧ (semiL Γ'' (↑r✝ φ)).comp Δ = semiR (↑Γ'' φ') r✝) ∨ ∃ Δ Δ', Δ φ = semiL Γ'' (↑r✝ φ) ∧ Δ' φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ Δ, Δ φ = semiL Γ'' (↑r✝ φ) ∧ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

iterate 2 ( first | refine ⟨(fun x => commaL _ _),rfl,?_⟩ | refine ⟨(fun x => commaR _ _),rfl,?_⟩ | refine ⟨(fun x => semiL _ _),rfl,?_⟩ | refine ⟨(fun x => semiR _ _),rfl,?_⟩ )

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ Δ, Δ φ = semiL Γ'' (↑r✝ φ) ∧ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

intro ψ ψ'

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ψ ψ' : Bunch P ⊢ ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

simp

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ψ ψ' : Bunch P ⊢ ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

( first | refine ⟨(fun x => commaL _ _),rfl,?_⟩ | refine ⟨(fun x => commaR _ _),rfl,?_⟩ | refine ⟨(fun x => semiL _ _),rfl,?_⟩ | refine ⟨(fun x => semiR _ _),rfl,?_⟩ )

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

first | refine ⟨(fun x => commaL _ _),rfl,?_⟩ | refine ⟨(fun x => commaR _ _),rfl,?_⟩ | refine ⟨(fun x => semiL _ _),rfl,?_⟩ | refine ⟨(fun x => semiR _ _),rfl,?_⟩

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

refine ⟨(fun x => commaL _ _),rfl,?_⟩

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ Δ, Δ φ = commaL Γ'' (↑r✝ φ) ∧ ∃ x, x φ' = commaR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ x, x φ' = commaR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

refine ⟨(fun x => commaR _ _),rfl,?_⟩

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ x, x φ' = commaR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => commaL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => commaR (↑Γ'' x) r✝) ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

refine ⟨(fun x => semiL _ _),rfl,?_⟩

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ Δ, Δ φ = semiL Γ'' (↑r✝ φ) ∧ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(x ψ') ψ

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.eq_inv

[198, 1]

[239, 13]

refine ⟨(fun x => semiR _ _),rfl,?_⟩

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∃ x, x φ' = semiR (↑Γ'' φ') r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑(x ψ') ψ

case refl P : Sort u_1 φ φ' : Bunch P r✝ : BunchWithHole P ih : ∀ {Γ' : BunchWithHole P}, ↑r✝ φ = ↑Γ' φ' → (∃ Δ, φ = ↑Δ φ' ∧ r✝.comp Δ = Γ') ∨ (∃ Δ, φ' = ↑Δ φ ∧ Γ'.comp Δ = r✝) ∨ ∃ Δ Δ', Δ φ = Γ' ∧ Δ' φ' = r✝ ∧ ∀ (ψ ψ' : Bunch P), ↑(Δ ψ) ψ' = ↑(Δ' ψ') ψ Γ'' : BunchWithHole P ⊢ ∀ (ψ ψ' : Bunch P), ↑((fun x => semiL Γ'' (↑r✝ x)) ψ) ψ' = ↑((fun x => semiR (↑Γ'' x) r✝) ψ') ψ

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.idem

[241, 9]

[243, 21]

simp [FunLike.coe]

P : Sort u_1 Γ : BunchWithHole P b : Bunch P ⊢ ↑Γ b = b ↔ Γ = hole

no goals

https://github.com/JamesGallicchio/brunched-invitations.git

3082c5ae68d2022b1439310f315a0038dae24e0c

BunchImpl/Bunch.lean

BunchImpl.BunchWithHole.idem'

[245, 9]

[247, 21]

simp [FunLike.coe]

P : Sort u_1 Γ : BunchWithHole P b : Bunch P ⊢ b = ↑Γ b ↔ Γ = hole

no goals