P_FUN_EQ_CONV
PairRules.P_FUN_EQ_CONV : (term -> conv)
Performs extensionality conversion for functions (function equality).
The conversion P_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 paired variable structure "p" and
equation "f = g", where p is of type ty1 and f and g are
functions of type ty1->ty2, a call to P_FUN_EQ_CONV "p" "f = g"
returns the theorem:
|- (f = g) = (!p. f p = g p)
Failure
P_FUN_EQ_CONV p tm fails if p is not a paired structure of variables
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
pair x must have type ty1; otherwise the conversion fails. Finally,
failure also occurs if any of the variables in p is free in either f
or g.