diff --git a/theories/base/at_cas.v b/theories/base/at_cas.v index c6df76454968deff070614172f9a315986d119ad..c1b20371d17ee11f0095a37d8b2cae9cab1a0d0c 100644 --- a/theories/base/at_cas.v +++ b/theories/base/at_cas.v @@ -11,7 +11,7 @@ Lemma f_CAS `{fG : !foundationG Σ} π V l h (v_r v_w: Z): ∗ ( ⌜b = true⌝ ∗ ⌜v = v_r⌝ ∗ ⌜value_at h' V' (VInj v_w)⌝ ∗ ⌜h' ≡ {[VInj v_w, V']} ∪ h⌝ - ∗ ⌜h ⊥ {[VInj v_w, V']}⌝ + ∗ ⌜h ## {[VInj v_w, V']}⌝ ∗ ⌜init l h'⌝ ∗ ⌜adj_opt (V1 !! l) (V' !! l)⌝ ∗ ⌜no_adj_right l h V1⌝ diff --git a/theories/base/at_fai.v b/theories/base/at_fai.v index 7c63dfe9d37a0236e156d7c5f113486b9055ae7c..1f3454957e4f4afee667eb62e99e7aebe2d0673e 100644 --- a/theories/base/at_fai.v +++ b/theories/base/at_fai.v @@ -11,7 +11,7 @@ Lemma f_FAI `{fG : !foundationG Σ} C π V l h: ∗ ⌜v' = (v + 1) `mod` Z.pos C⌝%Z ∗ ⌜value_at h' V' (VInj v')⌝ ∗ ⌜h' ≡ {[VInj v', V']} ∪ h⌝ - ∗ ⌜h ⊥ {[VInj v', V']}⌝ + ∗ ⌜h ## {[VInj v', V']}⌝ ∗ ⌜init l h'⌝ ∗ ⌜adj_opt (V1 !! l) (V' !! l)⌝ ∗ ⌜no_adj_right l h V1⌝ }}}. diff --git a/theories/base/at_shared.v b/theories/base/at_shared.v index 4f2aacce28c6492bfd5993b43e44f15346e4ae15..bdfdcbf9de60739ef8460947e40a678b15ba591d 100644 --- a/theories/base/at_shared.v +++ b/theories/base/at_shared.v @@ -22,7 +22,7 @@ Lemma write_at_update_hist ς ς' (V: View) h t l v (m: message) (VInj v, mview m) ∈ h' ∧ h' ≡ map_vt (hist_from (mem ς') l t) ∧ h' ≡ {[VInj v, mview m]} ∪ h - ∧ h ⊥ {[VInj v, mview m]}. + ∧ h ## {[VInj v, mview m]}. Proof. destruct Safe as [v' [V_l [Hv'1 Hv'2]]]. assert (t ⊑ mtime m). diff --git a/theories/base/at_write.v b/theories/base/at_write.v index 626ec95f3738dbf98075ca38d9225086942d147e..eaf2569149e38ffa65a089385bab6b33cb7d2a9b 100644 --- a/theories/base/at_write.v +++ b/theories/base/at_write.v @@ -7,7 +7,7 @@ Lemma f_write_at `{fG : !foundationG Σ} π V_l l h v: ⌜V_l ⊑ V'⌝ ∗ Seen π V' ∗ Hist l h' ∗ ⌜init_local h' V'⌝ ∗ ⌜init l h'⌝ ∗ ⌜h' ≡ {[VInj v, V']} ∪ h⌝ - ∗ ⌜h ⊥ {[VInj v, V']}⌝ + ∗ ⌜h ## {[VInj v, V']}⌝ ∗ ⌜value_at h' V' (VInj v)⌝}}}. Proof. iIntros (Φ) "(#I & Seen & Hist & %) Post". diff --git a/theories/examples/circ_buffer.v b/theories/examples/circ_buffer.v index e7380fccb0a00c6788d786e76db6754347daffa5..e25d4e1dc72dff85ca855d6fad863a0ea81d578e 100644 --- a/theories/examples/circ_buffer.v +++ b/theories/examples/circ_buffer.v @@ -101,7 +101,7 @@ Section CircBuffer. iIntros "Toks". rewrite /pToks_from /pTok. rewrite -own_op pair_op. rewrite !/op !/cmra_op /=. - case (decide ({[Pos.of_succ_nat i]} ⊥ coPset_from_ex (S i))) => [_|ND]; + case (decide ({[Pos.of_succ_nat i]} ## coPset_from_ex (S i))) => [_|ND]; last first. { exfalso. apply ND, coPset_from_disjoint. } iApply (own_mono with "Toks"). apply prod_included. @@ -113,7 +113,7 @@ Section CircBuffer. Proof. iIntros "Toks". rewrite -own_op pair_op !/op !/cmra_op /=. - case (decide ({[Pos.of_succ_nat i]} ⊥ coPset_from_ex (S i))) => [_|ND]; + case (decide ({[Pos.of_succ_nat i]} ## coPset_from_ex (S i))) => [_|ND]; last first. { exfalso. apply ND, coPset_from_disjoint. } iApply (own_mono with "Toks"). apply prod_included. @@ -126,9 +126,9 @@ Section CircBuffer. Proof. iIntros "Toks". rewrite -own_op pair_op !/op !/cmra_op /= /ucmra_op /=. - case (decide (coPset_from_ex i ⊥ ∅)) =>[_|ND]; last first. + case (decide (coPset_from_ex i ## ∅)) =>[_|ND]; last first. { exfalso. apply ND. set_solver+. } - case (decide (∅ ⊥ coPset_from_ex i)) =>[_|ND]; last first. + case (decide (∅ ## coPset_from_ex i)) =>[_|ND]; last first. { exfalso. apply ND. set_solver+. } iApply (own_mono with "Toks"). apply prod_included. rewrite /= !coPset_disj_included. set_solver+. diff --git a/theories/examples/nat_tokens.v b/theories/examples/nat_tokens.v index c1ffb8149f53e99f153b99970dc0d79a009331c1..c3611e7898620cfd9a5e839341a090039c9c59c8 100644 --- a/theories/examples/nat_tokens.v +++ b/theories/examples/nat_tokens.v @@ -36,7 +36,7 @@ Proof. Qed. Lemma coPset_from_disjoint i: - {[Pos.of_succ_nat i]} ⊥ coPset_from_ex (S i). + {[Pos.of_succ_nat i]} ## coPset_from_ex (S i). Proof. apply disjoint_singleton_l. rewrite coPset_from_ex_gt SuccNat2Pos.id_succ. lia. Qed. @@ -57,7 +57,7 @@ Proof. Qed. Lemma coPset_of_gset_difference_union (X Y Z: gset positive) - (Disj: Y ⊥ Z) (Sub: Y ⊆ X): + (Disj: Y ## Z) (Sub: Y ⊆ X): coPset.of_gset (X ∖ Z) = coPset.of_gset (X ∖ (Y ∪ Z)) ∪ coPset.of_gset Y. Proof. apply leibniz_equiv. move => x. @@ -71,14 +71,14 @@ Proof. Qed. Lemma coPset_of_gset_difference_disjoint (X Y Z: gset positive): - coPset.of_gset (X ∖ (Y ∪ Z)) ⊥ coPset.of_gset Y. + coPset.of_gset (X ∖ (Y ∪ Z)) ## coPset.of_gset Y. Proof. rewrite elem_of_disjoint. move => x. rewrite !coPset.elem_of_of_gset elem_of_difference elem_of_union. set_solver. Qed. -Lemma coPset_of_gset_top_difference (X Y: gset positive) (Disj: X ⊥ Y): +Lemma coPset_of_gset_top_difference (X Y: gset positive) (Disj: X ## Y): ⊤ ∖ coPset.of_gset X = (⊤ ∖ coPset.of_gset (Y ∪ X)) ∪ coPset.of_gset Y. Proof. apply leibniz_equiv. move => x. @@ -90,7 +90,7 @@ Proof. Qed. Lemma coPset_of_gset_top_disjoint (X Y: gset positive): - (⊤ ∖ coPset.of_gset (Y ∪ X)) ⊥ coPset.of_gset Y. + (⊤ ∖ coPset.of_gset (Y ∪ X)) ## coPset.of_gset Y. Proof. rewrite elem_of_disjoint. move => x. rewrite elem_of_difference coPset_of_gset_union. set_solver. diff --git a/theories/examples/rcu.v b/theories/examples/rcu.v index f819593391821116f7a26dd6c05a96d543cf2437..b2add99bc4f3f9764d9766378bf2d813dae090af 100644 --- a/theories/examples/rcu.v +++ b/theories/examples/rcu.v @@ -353,7 +353,7 @@ Section RCU. ⊢ own γ {[ t := CoPset (⊤ ∖ coPset.of_gset Y) ]} ∗ own γ {[ t := CoPset $ coPset.of_gset (Y ∖ X) ]}. Proof. - have Hj: (X ⊥ Y ∖ X) by set_solver+. + have Hj: (X ## Y ∖ X) by set_solver+. rewrite (coPset_of_gset_top_difference _ _ Hj) -coPset_disj_union; last apply coPset_of_gset_top_disjoint. rewrite (union_comm_L (Y ∖ X)) -union_difference_L; last auto. diff --git a/theories/examples/ticket_lock.v b/theories/examples/ticket_lock.v index 5d2715bd3c2dae8256a6d3d17b6e6a9f28c0b593..4d3dca206224cc297134f0f9dcb6e16fc1d470b8 100644 --- a/theories/examples/ticket_lock.v +++ b/theories/examples/ticket_lock.v @@ -367,7 +367,7 @@ Section TicketLock. Proof. iIntros "Perms". rewrite -own_op pair_op. rewrite !/op /cmra_op /=. - case (decide ({[Pos.of_succ_nat t]} ⊥ coPset_from_ex (S t))) => [_|ND]; + case (decide ({[Pos.of_succ_nat t]} ## coPset_from_ex (S t))) => [_|ND]; last first. { exfalso. apply ND, coPset_from_disjoint. } iApply (own_mono with "Perms"). apply prod_included. diff --git a/theories/gps/shared.v b/theories/gps/shared.v index c27359ddacd634a0e67ca1799437e2bf94f592c7..d48730625dfb0f72c66d76769d8d72978e3862dc 100644 --- a/theories/gps/shared.v +++ b/theories/gps/shared.v @@ -189,7 +189,7 @@ Section Setup. Persistent (PrtSeen γ s V) := _. Lemma StateInjection_insert s v V h ζ - (Cons: Consistent ζ h) (SI: StateInjection ζ) (HDisj: h ⊥ {[VInj v,V]}) + (Cons: Consistent ζ h) (SI: StateInjection ζ) (HDisj: h ## {[VInj v,V]}) : StateInjection ({[s, (v, V)]} ∪ ζ). Proof. move => e1 e2 /elem_of_union [/elem_of_singleton ->| In1] diff --git a/theories/lang/blocks.v b/theories/lang/blocks.v index 2aec0036251c92aac81e39a0b3e9afeadc38dd53..922d36b3ece8927afa0ba0dc713c3ee5eef3eeb6 100644 --- a/theories/lang/blocks.v +++ b/theories/lang/blocks.v @@ -54,7 +54,7 @@ Section GHist. Lemma gblock_ends_ins_update x h p (OK: hTime_ok x ({[p]} ∪ h)) - (Fresh: h ⊥ {[p]}) + (Fresh: h ## {[p]}) : gblock_ends_ins x h p (gblock_ends x h) (gblock_ends x ({[p]} ∪ h)). Proof. apply block_ends_ins. diff --git a/theories/rsl/rsl.v b/theories/rsl/rsl.v index a790e4a57bb7d5245e24236eba63b2e1f3eb7b89..0886f1b8be52f99b3ea886dd0ee1b3d810d99569 100644 --- a/theories/rsl/rsl.v +++ b/theories/rsl/rsl.v @@ -121,7 +121,7 @@ Instance InitRaw_persistent V jγ : Persistent (InitRaw V jγ) := _. Lemma big_sepS_gblock_ends_ins_update l (h: History) p0 (Ψ: Val * View → iProp) - (Disj: (h ⊥ {[p0]})%C) + (Disj: (h ## {[p0]})%C) (GB: gblock_ends_ins l h p0 (gblock_ends l h) (gblock_ends l ({[p0]} ∪ h))) : Ψ p0 ∗ ([∗ set] p ∈ gblock_ends l h, Ψ p) ⊢ ([∗ set] p ∈ gblock_ends l ({[p0]} ∪ h), Ψ p). diff --git a/theories/rsl/rsl_sts.v b/theories/rsl/rsl_sts.v index da40162ba0182eb6cc2a1c6a08293b6725895fe4..eca760c260e611fec5ee3dbeb93701e11dc96db2 100644 --- a/theories/rsl/rsl_sts.v +++ b/theories/rsl/rsl_sts.v @@ -295,15 +295,15 @@ Proof. Qed. (** Properties of split **) -Lemma tok_disj_state_singleton s i: i ∈ rISet2 s → sts.tok s ⊥ {[Change i]}. +Lemma tok_disj_state_singleton s i: i ∈ rISet2 s → sts.tok s ## {[Change i]}. Proof. abstract set_solver. Qed. Lemma state_ISet_split_token_disj_1 i1 i2 i s: - sts.tok (state_ISet_split i1 i2 i s) ⊥ {[Change i1]}. + sts.tok (state_ISet_split i1 i2 i s) ## {[Change i1]}. Proof. apply tok_disj_state_singleton. destruct s; abstract set_solver+. Qed. Lemma state_ISet_split_token_disj_2 i1 i2 i s: - sts.tok (state_ISet_split i1 i2 i s) ⊥ {[Change i2]}. + sts.tok (state_ISet_split i1 i2 i s) ## {[Change i2]}. Proof. apply tok_disj_state_singleton. destruct s; abstract set_solver+. Qed. Lemma state_ISet_split_included_1 i1 i2 i s: diff --git a/theories/viewpred/viewpred.v b/theories/viewpred/viewpred.v index 9a12a7753abd112422dc3fc2b53ac8f0d628ae13..8b1f587a74da24b802345ce29390744beb76b595 100644 --- a/theories/viewpred/viewpred.v +++ b/theories/viewpred/viewpred.v @@ -286,7 +286,7 @@ Notation "∀ x .. y , P" := (vPred_forall (λ x, .. (vPred_forall (λ y, P%VP)) Notation "∃ x .. y , P" := (vPred_exists (λ x, .. (vPred_exists (λ y, P%VP)) ..)) : vPred_scope. Notation "P ∗ Q" := (vPred_sep P Q) : vPred_scope. Notation "x = y" := (vPred_pure (x%C%type = y%C%type)) : vPred_scope. -Notation "x ⊥ y" := (vPred_pure (x%C%type ⊥ y%C%type)) : vPred_scope. +Notation "x ## y" := (vPred_pure (x%C%type ## y%C%type)) : vPred_scope. Notation "'False'" := (vPred_pure False) : vPred_scope. Notation "'True'" := (vPred_pure True) : vPred_scope. Infix "∧" := vPred_and : vPred_scope.