PFORALL_EQ

PairRules.PFORALL_EQ : (term -> thm -> thm)

Universally quantifies both sides of an equational theorem.

When applied to a paired structure of variables p and a theorem

    A |- t1 = t2

whose conclusion is an equation between boolean terms:

    PFORALL_EQ

returns the theorem:

    A |- (!p. t1) = (!p. t2)

unless any of the variables in p is free in any of the assumptions.

          A |- t1 = t2
   --------------------------  PFORALL_EQ "p"      [where p is not free in A]
    A |- (!p. t1) = (!p. t2)

Failure

Fails if the theorem is not an equation between boolean terms, or if the supplied term is not a paired structure of variables, or if any of the variables in the supplied pair is free in any of the assumptions.

See also

Drule.FORALL_EQ, PairRules.PEXISTS_EQ, PairRules.PSELECT_EQ