Commit bcc8b376 authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Document BI axioms in terms of the axioms in the ordered RA model.

parent 33620b9d
......@@ -112,20 +112,27 @@ Section bi_mixin.
bi_mixin_plainly_absorbing P Q : bi_plainly P Q bi_plainly P;
(* Persistently *)
(* In the ordered RA model: `core` is monotone *)
bi_mixin_persistently_mono P Q :
(P Q) bi_persistently P bi_persistently Q;
(* In the ordered RA model: `core` is idempotent *)
bi_mixin_persistently_idemp_2 P :
bi_persistently P bi_persistently (bi_persistently P);
bi_mixin_plainly_persistently_1 P :
bi_plainly (bi_persistently P) bi_plainly P;
(* In the ordered RA model [P ⊢ □ emp] (which can currently still be derived
from the plainly axioms, which will be removed): `ε ≼ core x` *)
bi_mixin_persistently_forall_2 {A} (Ψ : A PROP) :
( a, bi_persistently (Ψ a)) bi_persistently ( a, Ψ a);
bi_mixin_persistently_exist_1 {A} (Ψ : A PROP) :
bi_persistently ( a, Ψ a) a, bi_persistently (Ψ a);
(* In the ordered RA model: [x ≼ₑₓₜ y → core x ≼ core y] *)
bi_mixin_persistently_absorbing P Q :
bi_persistently P Q bi_persistently P;
(* In the ordered RA model: [ε ≼ core x] *)
bi_mixin_persistently_and_sep_elim P Q :
bi_persistently P Q (emp P) Q;
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