LEFT_IMP_PFORALL_CONV

PairRules.LEFT_IMP_PFORALL_CONV : conv

Moves a paired universal quantification of the antecedent outwards through an implication.

When applied to a term of the form (!p. t) ==> u, the conversion LEFT_IMP_PFORALL_CONV returns the theorem:

   |- (!p. t) ==> u = (?p'. t[p'/p] ==> u)

where p' is a primed variant of the pair p that does not contain any variables that appear free in the input term.

Failure

Fails if applied to a term not of the form (!p. t) ==> u.

See also

Conv.LEFT_IMP_FORALL_CONV, PairRules.PEXISTS_IMP_CONV, PairRules.RIGHT_IMP_PFORALL_CONV