Standard Library | The Coq Proof Assistant

The Coq Proof Assistant

# Library Coq.ZArith.Zmax

THIS FILE IS DEPRECATED.
Require Export BinInt Zcompare Zorder.
Local Open Scope Z_scope.
Definition Z.max is now BinInt.Z.max.
Exact compatibility
Notation Zmax_right := Z.max_r (only parsing).
Notation Zle_max_compat_r := Z.max_le_compat_r (only parsing).
Notation Zle_max_compat_l := Z.max_le_compat_l (only parsing).
Notation Zmax_idempotent := Z.max_id (only parsing).
Notation Zmax_n_n := Z.max_id (only parsing).
Notation Zmax_irreducible_dec := Z.max_dec (only parsing).
Notation Zmax_le_prime := Z.max_le (only parsing).
Notation Zmax_SS := Z.succ_max_distr (only parsing).
Notation Zplus_max_distr_l := Z.add_max_distr_l (only parsing).
Notation Zplus_max_distr_r := Z.add_max_distr_r (only parsing).
Notation Zmax_plus := Z.add_max_distr_r (only parsing).
Notation Zmax1 := Z.le_max_l (only parsing).
Notation Zmax2 := Z.le_max_r (only parsing).
Notation Zmax_irreducible_inf := Z.max_dec (only parsing).
Notation Zmax_le_prime_inf := Z.max_le (only parsing).
Notation Zpos_max := Pos2Z.inj_max (only parsing).
Notation Zpos_minus := Pos2Z.inj_sub_max (only parsing).
Slightly different lemmas
Lemma Zmax_spec x y :
x >= y /\ Z.max x y = x \/ x < y /\ Z.max x y = y.
Lemma Zmax_left n m : n>=m -> Z.max n m = n.
Lemma Zpos_max_1 p : Z.max 1 (Z.pos p) = Z.pos p.