LEFT_AND_FORALL_CONV

Conv.LEFT_AND_FORALL_CONV : conv

Moves a universal quantification of the left conjunct outwards through a conjunction.

When applied to a term of the form (!x.P) /\ Q, the conversion LEFT_AND_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.AND_FORALL_CONV, Conv.FORALL_AND_CONV, Conv.RIGHT_AND_FORALL_CONV