EXISTS_EQ : (term -> thm -> thm)
STRUCTURE
Drule
SYNOPSIS
Existentially quantifies both sides of an equational theorem.
DESCRIPTION
When applied to a variable x and a theorem whose conclusion is equational, A |- t1 = t2, the inference rule EXISTS_EQ returns the theorem A |- (?x. t1) = (?x. t2), provided the variable x is not free in any of the assumptions. 
         A |- t1 = t2
   ------------------------  EXISTS_EQ "x"      [where x is not free in A]
    A |- (?x.t1) = (?x.t2)

FAILURE
Fails unless the theorem is equational with both sides having type bool, or if the term is not a variable, or if the variable to be quantified over is free in any of the assumptions.
SEEALSO
AP_TERM, EXISTS_IMP, FORALL_EQ, MK_EXISTS, SELECT_EQ
HOL  Kananaskis-13