File: EXT.doc

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\DOC EXT

\TYPE {EXT : (thm -> thm)}

\SYNOPSIS
Derives equality of functions from extentional equivalence.

\KEYWORDS
rule, extentionality.

\DESCRIBE
When applied to a theorem {A |- !x. t1 x = t2 x}, the inference rule
{EXT} returns the theorem {A |- t1 = t2}.
{
    A |- !x. t1 x = t2 x
   ----------------------  EXT          [where x is not free in t1 or t2]
        A |- t1 = t2
}
\FAILURE
Fails if the theorem does not have the form indicated above, or
if the variable {x} is free either of the functions {t1} or {t2}.

\SEEALSO
AP_THM, ETA_CONV, FUN_EQ_CONV.

\ENDDOC