ZF: NEW DEFINITION OF PI(A,B)
Was Pi(A,B) == {f: Pow(Sigma(A,B)). ALL x:A. EX! y. <x,y>: f}
Now function(r) == ALL x y. <x,y>:r --> (ALL y'. <x,y'>:r --> y=y')
Pi(A,B) == {f: Pow(Sigma(A,B)). A<=domain(f) & function(f)}"
This simplifies many proofs, since (a) the top-level definition has fewer
bound variables (b) the "total" and "function" properties are separated
(c) the awkward EX! quantifier is eliminated.
ZF/ZF.thy/function: new definition
#! /bin/sh
# teeinput -- start a program and log all inputs to a file
# environment variable $LISTEN specifies the file name
tee -a -i $LISTEN | $*