diff options
Diffstat (limited to 'theories/Arith/Lt.v')
| -rw-r--r-- | theories/Arith/Lt.v | 26 |
1 files changed, 13 insertions, 13 deletions
diff --git a/theories/Arith/Lt.v b/theories/Arith/Lt.v index f824ee6f..bfc2b91a 100644 --- a/theories/Arith/Lt.v +++ b/theories/Arith/Lt.v @@ -25,7 +25,7 @@ Local Open Scope nat_scope. Notation lt_irrefl := Nat.lt_irrefl (compat "8.4"). (* ~ x < x *) -Hint Resolve lt_irrefl: arith v62. +Hint Resolve lt_irrefl: arith. (** * Relationship between [le] and [lt] *) @@ -44,9 +44,9 @@ Proof. apply Nat.lt_succ_r. Qed. -Hint Immediate lt_le_S: arith v62. -Hint Immediate lt_n_Sm_le: arith v62. -Hint Immediate le_lt_n_Sm: arith v62. +Hint Immediate lt_le_S: arith. +Hint Immediate lt_n_Sm_le: arith. +Hint Immediate le_lt_n_Sm: arith. Theorem le_not_lt n m : n <= m -> ~ m < n. Proof. @@ -58,7 +58,7 @@ Proof. apply Nat.lt_nge. Qed. -Hint Immediate le_not_lt lt_not_le: arith v62. +Hint Immediate le_not_lt lt_not_le: arith. (** * Asymmetry *) @@ -79,8 +79,8 @@ Proof. intros. now apply Nat.neq_sym, Nat.neq_0_lt_0. Qed. -Hint Resolve lt_0_Sn lt_n_0 : arith v62. -Hint Immediate neq_0_lt lt_0_neq: arith v62. +Hint Resolve lt_0_Sn lt_n_0 : arith. +Hint Immediate neq_0_lt lt_0_neq: arith. (** * Order and successor *) @@ -97,8 +97,8 @@ Proof. apply Nat.succ_lt_mono. Qed. -Hint Resolve lt_n_Sn lt_S lt_n_S : arith v62. -Hint Immediate lt_S_n : arith v62. +Hint Resolve lt_n_Sn lt_S lt_n_S : arith. +Hint Immediate lt_S_n : arith. (** * Predecessor *) @@ -117,8 +117,8 @@ Proof. intros. now apply Nat.lt_pred_l, Nat.neq_0_lt_0. Qed. -Hint Immediate lt_pred: arith v62. -Hint Resolve lt_pred_n_n: arith v62. +Hint Immediate lt_pred: arith. +Hint Resolve lt_pred_n_n: arith. (** * Transitivity properties *) @@ -126,7 +126,7 @@ Notation lt_trans := Nat.lt_trans (compat "8.4"). Notation lt_le_trans := Nat.lt_le_trans (compat "8.4"). Notation le_lt_trans := Nat.le_lt_trans (compat "8.4"). -Hint Resolve lt_trans lt_le_trans le_lt_trans: arith v62. +Hint Resolve lt_trans lt_le_trans le_lt_trans: arith. (** * Large = strict or equal *) @@ -139,7 +139,7 @@ Qed. Notation lt_le_weak := Nat.lt_le_incl (compat "8.4"). -Hint Immediate lt_le_weak: arith v62. +Hint Immediate lt_le_weak: arith. (** * Dichotomy *) |