Commit 5c639877 authored by Ralf Jung's avatar Ralf Jung

note that forall_2 would be derivable in a classical meta-logic

parent 8389920e
...@@ -58,7 +58,7 @@ Section bi_mixin. ...@@ -58,7 +58,7 @@ Section bi_mixin.
bi_mixin_entails_po : PreOrder bi_entails; bi_mixin_entails_po : PreOrder bi_entails;
bi_mixin_equiv_spec P Q : equiv P Q (P Q) (Q P); bi_mixin_equiv_spec P Q : equiv P Q (P Q) (Q P);
(* Non-expansiveness *) (** Non-expansiveness *)
bi_mixin_pure_ne n : Proper (iff ==> dist n) bi_pure; bi_mixin_pure_ne n : Proper (iff ==> dist n) bi_pure;
bi_mixin_and_ne : NonExpansive2 bi_and; bi_mixin_and_ne : NonExpansive2 bi_and;
bi_mixin_or_ne : NonExpansive2 bi_or; bi_mixin_or_ne : NonExpansive2 bi_or;
...@@ -71,9 +71,11 @@ Section bi_mixin. ...@@ -71,9 +71,11 @@ Section bi_mixin.
bi_mixin_wand_ne : NonExpansive2 bi_wand; bi_mixin_wand_ne : NonExpansive2 bi_wand;
bi_mixin_persistently_ne : NonExpansive bi_persistently; bi_mixin_persistently_ne : NonExpansive bi_persistently;
(* Higher-order logic *) (** Higher-order logic *)
bi_mixin_pure_intro P (φ : Prop) : φ P φ ; bi_mixin_pure_intro P (φ : Prop) : φ P φ ;
bi_mixin_pure_elim' (φ : Prop) P : (φ True P) φ P; bi_mixin_pure_elim' (φ : Prop) P : (φ True P) φ P;
(* This is actually derivable if we assume excluded middle in Coq,
via [(∀ a, φ a) ∨ (∃ a, ¬φ a)]. *)
bi_mixin_pure_forall_2 {A} (φ : A Prop) : ( a, φ a ) a, φ a ; bi_mixin_pure_forall_2 {A} (φ : A Prop) : ( a, φ a ) a, φ a ;
bi_mixin_and_elim_l P Q : P Q P; bi_mixin_and_elim_l P Q : P Q P;
...@@ -93,7 +95,7 @@ Section bi_mixin. ...@@ -93,7 +95,7 @@ Section bi_mixin.
bi_mixin_exist_intro {A} {Ψ : A PROP} a : Ψ a a, Ψ a; bi_mixin_exist_intro {A} {Ψ : A PROP} a : Ψ a a, Ψ a;
bi_mixin_exist_elim {A} (Φ : A PROP) Q : ( a, Φ a Q) ( a, Φ a) Q; bi_mixin_exist_elim {A} (Φ : A PROP) Q : ( a, Φ a Q) ( a, Φ a) Q;
(* BI connectives *) (** BI connectives *)
bi_mixin_sep_mono P P' Q Q' : (P Q) (P' Q') P P' Q Q'; bi_mixin_sep_mono P P' Q Q' : (P Q) (P' Q') P P' Q Q';
bi_mixin_emp_sep_1 P : P emp P; bi_mixin_emp_sep_1 P : P emp P;
bi_mixin_emp_sep_2 P : emp P P; bi_mixin_emp_sep_2 P : emp P P;
...@@ -102,7 +104,7 @@ Section bi_mixin. ...@@ -102,7 +104,7 @@ Section bi_mixin.
bi_mixin_wand_intro_r P Q R : (P Q R) P Q - R; bi_mixin_wand_intro_r P Q R : (P Q R) P Q - R;
bi_mixin_wand_elim_l' P Q R : (P Q - R) P Q R; bi_mixin_wand_elim_l' P Q R : (P Q - R) P Q R;
(* Persistently *) (** Persistently *)
(* In the ordered RA model: Holds without further assumptions. *) (* In the ordered RA model: Holds without further assumptions. *)
bi_mixin_persistently_mono P Q : (P Q) <pers> P <pers> Q; bi_mixin_persistently_mono P Q : (P Q) <pers> P <pers> Q;
(* In the ordered RA model: `core` is idempotent *) (* In the ordered RA model: `core` is idempotent *)
......
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