X_FUN_EQ_CONV : (term -> conv)
STRUCTURE
Conv
SYNOPSIS
Performs extensionality conversion for functions (function equality).
DESCRIPTION
The conversion X_FUN_EQ_CONV embodies the fact that two functions are equal precisely when they give the same results for all values to which they can be applied. For any variable "x" and equation "f = g", where x is of type ty1 and f and g are functions of type ty1->ty2, a call to X_FUN_EQ_CONV "x" "f = g" returns the theorem: 
   |- (f = g) = (!x. f x = g x)

FAILURE
X_FUN_EQ_CONV x tm fails if x is not a variable or if tm is not an equation f = g where f and g are functions. Furthermore, if f and g are functions of type ty1->ty2, then the variable x must have type ty1; otherwise the conversion fails. Finally, failure also occurs if x is free in either f or g.
SEEALSO
EXT, FUN_EQ_CONV
HOL  Kananaskis-13