EXISTS_INTRO_IMP

ConseqConv.EXISTS_INTRO_IMP : term -> thm -> thm

Existentially quantifies both sides of an implication in the conclusion of a theorem.

When applied to a term x and a theorem A |- t1 ==> t2, the inference rule EXISTS_INTRO_IMP returns the theorem A |- (?x. t1) ==> (?x. t2), provided x is a variable not free in any of the assumptions. There is no compulsion that x should be free in t1 or t2.

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

Failure

Fails if x is not a variable, the conclusion of the theorem is not an implication, or if x is free in any of the assumptions.

Example

   - val thm0 = mk_thm ([], Term `P (x:'a) ==> Q x`);
   > val thm0 =  |- P (x :'a) ==> Q x : thm

   - val thm1 = EXISTS_INTRO_IMP (Term `x:'a`) thm0;
   > val thm1 =  |- (?x. P x) ==> (?x. Q x)

See also

Thm.GEN, ConseqConv.GEN_IMP