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(** Theorems about [gt] in [nat].  This file is DEPRECATED now, see module [PeanoNat.Nat] instead, which favor [lt] over [gt].  [gt] is defined in [Init/Peano.v] as: << Definition gt (n m:nat) := m < n. >> *)
Local Open Scope nat_scope.
(** * Order and successor *)
Proof Nat.lt_0_succ _.
Proof Nat.lt_succ_diag_r _.

Lemma gt_S_n n m : S m > S n -> m > n.