LEFT_IMP_FORALL_CONV

Conv.LEFT_IMP_FORALL_CONV : conv

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

When applied to a term of the form (!x.P) ==> Q, the conversion LEFT_IMP_FORALL_CONV returns the theorem:

   |- (!x.P) ==> Q = (?x'. P[x'/x] ==> Q)

where x' is a primed variant of x that does not appear free in the input term.

Failure

Fails if applied to a term not of the form (!x.P) ==> Q.

See also

Conv.EXISTS_IMP_CONV, Conv.RIGHT_IMP_FORALL_CONV