LIST_MK_PFORALL

PairRules.LIST_MK_PFORALL : (term list -> thm -> thm)

Multiply universally quantifies both sides of an equation using the given pairs.

When applied to a list of terms [p1;...;pn], where the pi are all paired structures of variables, and a theorem A |- t1 = t2, the inference rule LIST_MK_PFORALL universally quantifies both sides of the equation using the pairs given, none of the variables in the pairs should be free in the assumption list.

                A |- t1 = t2
   --------------------------------------  LIST_MK_PFORALL ["x1";...;"xn"]
    A |- (!x1...xn. t1) = (!x1...xn. t2)

Failure

Fails if any term in the list is not a paired structure of variables, or if any variable is free in the assumption list, or if the theorem is not equational.

See also

Drule.LIST_MK_EXISTS, PairRules.PFORALL_EQ, PairRules.MK_PFORALL