Definition ex_maxn := m - ex_minn ex_maxn_subproof.

(* Specifications: *)
Lemma ex_maxnP : ex_maxn_spec ex_maxn.
Lemma eq_ex_minn P Q exP exQ : P =1 Q -> @ex_minn P exP = @ex_minn Q exQ.
Lemma eq_ex_maxn (P Q : pred nat) m n exP ubP exQ ubQ : P =1 Q -> @ex_maxn P m exP ubP = @ex_maxn Q n exQ ubQ.