theory John imports Complex_Main
begin

axiomatization
f :: "real => real" and
g :: "real => real" and
h :: "real => real" where
ax1: "EX x. ALL y. x ~= y --> h x > h y" and
ax2: "ALL x. (ALL y. x ~= y --> h x > h y) --> g x = 0"

lemma "EX x. g x = 0"
by (metis ax1 ax2)

end