EXISTS_IMP

Drule.EXISTS_IMP : (term -> thm -> thm)

Existentially quantifies both the antecedent and consequent of an implication.

When applied to a variable x and a theorem A |- t1 ==> t2, the inference rule EXISTS_IMP returns the theorem A |- (?x. t1) ==> (?x. t2), provided x is not free in the assumptions.

         A |- t1 ==> t2
   --------------------------  EXISTS_IMP "x"   [where x is not free in A]
    A |- (?x.t1) ==> (?x.t2)

Failure

Fails if the theorem is not implicative, or if the term is not a variable, or if the term is a variable but is free in the assumption list.

See also

Drule.EXISTS_EQ