GEN_IMP

ConseqConv.GEN_IMP : term -> thm -> thm

Generalizes 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 GEN_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)
   ----------------------------     GEN_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 = GEN_IMP (Term `x:'a`) thm0;
   > val thm1 =  |- (!x. P x) ==> (!x. Q x)

See also

Thm.GEN, ConseqConv.GEN_EQ