Conv.FORALL_IMP

STRUCTURE

SYNOPSIS

Moves a universal quantification inwards through an implication.

DESCRIPTION

When applied to a term of the form !x. P ==> Q, where x is not free in both P and Q, FORALL_IMP_CONV returns a theorem of one of three forms, depending on occurrences of the variable x in P and Q. If x is free in P but not in Q, then the theorem:

   |- (!x. P ==> Q) = (?x.P) ==> Q

is returned. If x is free in Q but not in P, then the result is:

   |- (!x. P ==> Q) = P ==> (!x.Q)

And if x is free in neither P nor Q, then the result is:

   |- (!x. P ==> Q) = (?x.P) ==> (!x.Q)

FAILURE

FORALL_IMP_CONV fails if it is applied to a term not of the form !x. P ==> Q, or if it is applied to a term !x. P ==> Q in which the variable x is free in both P and Q.

SEEALSO

LEFT_IMP_EXISTS_CONV, RIGHT_IMP_FORALL_CONV