Re: [isabelle] Using implications
I agree with your proof. But then, if it is to define how to *approximate*
a function f and a function g to be the same by comparing those x's and y's
c, then should the = operator be replaced here? It seems the problem here
is caused by overloading = with a form of approximated =, right? If so, how
should one go about introducing a new operator, say for approximation?
On Jan 26, 2011 6:23pm, Brian Huffman <brianh at cs.pdx.edu> wrote:
On Wed, Jan 26, 2011 at 10:14 AM, Eg Gloor egglue at gmail.com> wrote:
> S :: "real set" and
> foo :: "real => real" and
> bar :: "real => real" and
> bax :: "real => real" and
> c :: real
> where ax1: "ALL f g. (ALL x y. x > c & y > cfx = gy) --> f = g"
> and ax2: "ALL a b. bax a > c & bax b > c foo (bax a) = bar (bax b)"
Once again, we see that axioms are evil. Your ax1 is already
inconsistent all by itself:
let ?f = "%x::real. if x > c then (0::real) else 1"
let ?g = "%x::real. if x > c then (0::real) else 2"
have "?f = ?g"
by (rule ax1 [rule_format], simp)
hence "?fc = ?g c"
by (rule arg_cong)
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