SELECT_EQ : (term -> thm -> thm)

SYNOPSIS
Applies epsilon abstraction to both terms of an equation.

DESCRIBE
Effects the extensionality of the epsilon operator @.
       A |- t1 = t2
   ------------------------  SELECT_EQ "x"      [where x is not free in A]
    A |- (@x.t1) = (@x.t2)

FAILURE
Fails if the conclusion of the theorem is not an equation, or if the variable x is free in A.

EXAMPLE
Given a theorem which shows the equivalence of two distinct forms of defining the property of being an even number:
   th = |- (x MOD 2 = 0) = (?y. x = 2 * y)
A theorem giving the equivalence of the epsilon abstraction of each form is obtained:
   #SELECT_EQ "x:num" th;;
   |- (@x. x MOD 2 = 0) = (@x. ?y. x = 2 * y)

SEEALSO  ABS,   AP_TERM,   EXISTS_EQ,   FORALL_EQ,   SELECT_AX,   SELECT_CONV,   SELECT_ELIM,   SELECT_INTRO

HOL  Kananaskis 0