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Commit e5905932 authored by Robbert Krebbers's avatar Robbert Krebbers
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Rename `laterN_plus` into `laterN_add`.

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...@@ -163,7 +163,7 @@ Section positive. ...@@ -163,7 +163,7 @@ Section positive.
Local Instance pos_validN_instance : ValidN positive := λ n x, True. Local Instance pos_validN_instance : ValidN positive := λ n x, True.
Local Instance pos_pcore_instance : PCore positive := λ x, None. Local Instance pos_pcore_instance : PCore positive := λ x, None.
Local Instance pos_op_instance : Op positive := Pos.add. Local Instance pos_op_instance : Op positive := Pos.add.
Definition pos_op_plus x y : x y = (x + y)%positive := eq_refl. Definition pos_op_add x y : x y = (x + y)%positive := eq_refl.
Lemma pos_included (x y : positive) : x y (x < y)%positive. Lemma pos_included (x y : positive) : x y (x < y)%positive.
Proof. by rewrite Plt_sum. Qed. Proof. by rewrite Plt_sum. Qed.
Lemma pos_ra_mixin : RAMixin positive. Lemma pos_ra_mixin : RAMixin positive.
......
...@@ -183,7 +183,7 @@ Lemma later_laterN n P : ▷^(S n) P ⊣⊢ ▷ ▷^n P. ...@@ -183,7 +183,7 @@ Lemma later_laterN n P : ▷^(S n) P ⊣⊢ ▷ ▷^n P.
Proof. done. Qed. Proof. done. Qed.
Lemma laterN_later n P : ▷^(S n) P ⊣⊢ ▷^n P. Lemma laterN_later n P : ▷^(S n) P ⊣⊢ ▷^n P.
Proof. induction n; f_equiv/=; auto. Qed. Proof. induction n; f_equiv/=; auto. Qed.
Lemma laterN_plus n1 n2 P : ▷^(n1 + n2) P ⊣⊢ ▷^n1 ▷^n2 P. Lemma laterN_add n1 n2 P : ▷^(n1 + n2) P ⊣⊢ ▷^n1 ▷^n2 P.
Proof. induction n1; f_equiv/=; auto. Qed. Proof. induction n1; f_equiv/=; auto. Qed.
Lemma laterN_le n1 n2 P : n1 n2 ▷^n1 P ▷^n2 P. Lemma laterN_le n1 n2 P : n1 n2 ▷^n1 P ▷^n2 P.
Proof. induction 1; simpl; by rewrite -?later_intro. Qed. Proof. induction 1; simpl; by rewrite -?later_intro. Qed.
......
...@@ -288,7 +288,7 @@ Global Instance into_laterN_later only_head n n' m' P Q lQ : ...@@ -288,7 +288,7 @@ Global Instance into_laterN_later only_head n n' m' P Q lQ :
Proof. Proof.
rewrite /MakeLaterN /IntoLaterN /MaybeIntoLaterN /NatCancel. rewrite /MakeLaterN /IntoLaterN /MaybeIntoLaterN /NatCancel.
move=> Hn [_ ->|->] <-; move=> Hn [_ ->|->] <-;
by rewrite -later_laterN -laterN_plus -Hn Nat.add_comm. by rewrite -later_laterN -laterN_add -Hn Nat.add_comm.
Qed. Qed.
Global Instance into_laterN_laterN only_head n m n' m' P Q lQ : Global Instance into_laterN_laterN only_head n m n' m' P Q lQ :
NatCancel n m n' m' NatCancel n m n' m'
...@@ -297,7 +297,7 @@ Global Instance into_laterN_laterN only_head n m n' m' P Q lQ : ...@@ -297,7 +297,7 @@ Global Instance into_laterN_laterN only_head n m n' m' P Q lQ :
IntoLaterN only_head n (▷^m P) lQ | 1. IntoLaterN only_head n (▷^m P) lQ | 1.
Proof. Proof.
rewrite /MakeLaterN /IntoLaterN /MaybeIntoLaterN /NatCancel. rewrite /MakeLaterN /IntoLaterN /MaybeIntoLaterN /NatCancel.
move=> Hn [_ ->|->] <-; by rewrite -!laterN_plus -Hn Nat.add_comm. move=> Hn [_ ->|->] <-; by rewrite -!laterN_add -Hn Nat.add_comm.
Qed. Qed.
Global Instance into_laterN_and_l n P1 P2 Q1 Q2 : Global Instance into_laterN_and_l n P1 P2 Q1 Q2 :
......
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