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Text Generation
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Text
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language-modeling
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English
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100K - 1M
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File size: 451 Bytes
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horizon := 1;;
thm `;
let R be num->num->bool;
assume !x. R x x [1];
assume !x y z. R x y /\ R y z ==> R x z [2];
thus (!m n. m <= n ==> R m n) <=> (!n. R n (SUC n))
proof
now [3] // back direction first
assume !n. R n (SUC n);
let m n be num;
!d. R m (m + d) ==> R m (m + SUC d) [4] by 2,ADD_CLAUSES;
R m (m + 0) by 1,ADD_CLAUSES;
!d. R m (m + d) by 4,INDUCT_TAC;
thus m <= n ==> R m n by LE_EXISTS;
end;
!n. n <= SUC n;
qed by 3`;;
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