formal/hol/Help/ALL_TAC.doc

\DOC ALL_TAC

\TYPE {ALL_TAC : tactic}

\SYNOPSIS
Passes on a goal unchanged.

\KEYWORDS
tactic, identity.

\DESCRIBE
{ALL_TAC} applied to a goal {g} simply produces the subgoal list {[g]}. It is
the identity for the {THEN} tactical.

\FAILURE
Never fails.

\EXAMPLE
Suppose we want to solve the goal:
{
  # g `~(n MOD 2 = 0) <=> n MOD 2 = 1`;;
  ...
}
We could just solve it with {e ARITH_TAC}, but suppose we want to introduce a
little lemma that {n MOD 2 < 2}, proving that by {ARITH_TAC}. We could do
{
  # e(SUBGOAL_THEN `n MOD 2 < 2` ASSUME_TAC THENL
       [ARITH_TAC;
        ...rest of proof...]);;
}
However if we split off many lemmas, we get a deeply nested proof structure
that's a bit confusing. In cases where the proofs of the lemmas are trivial
one-liners like this we might just want to keep the proof basically linear with
{
  # e(SUBGOL_THEN `n MOD 2 < 2` ASSUME_TAC THENL [ARITH_TAC; ALL_TAC] THEN
      ...rest of proof...);;
}

\USES
Keeping proof structures linear, as in the above example, or convenient
algebraic combinations in complicated tactic structures.

\SEEALSO
NO_TAC, REPEAT, THENL.

\ENDDOC