[isabelle] A simple lemma



Hi,

Does anyone know why the following lemma is provable?

lemma "F = G --> (EX a b. a ~= b --> F a = G a & F b ~= G b)"
by auto

If F and G are equal, then F x = G x for all x. So how come the above
is provable?

Thanks a lot for your time.

John





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