diff --git a/theories/bi/embedding.v b/theories/bi/embedding.v index 176a12da7b654a80a1fd9badb8b99cdc2b0c8f22..24f4c237f29151889720cc74c3656b67cc75e8e8 100644 --- a/theories/bi/embedding.v +++ b/theories/bi/embedding.v @@ -17,6 +17,11 @@ Record BiEmbedMixin (PROP1 PROP2 : bi) `(Embed PROP1 PROP2) := { bi_embed_mixin_mono : Proper ((⊢) ==> (⊢)) (embed (A:=PROP1) (B:=PROP2)); bi_embed_mixin_emp_valid_inj (P : PROP1) : (⊢@{PROP2} ⎡P⎤) → ⊢ P; + (** The following axiom expresses that the embedding is injective in the OFE + sense. Instead of this axiom being expressed in terms of [siProp] or + externally (i.e., as [Inj (dist n) (dist n) embed]), it is expressed using the + internal equality of _any other_ BI [PROP']. This is more general, as we do + not have any machinary to embed [siProp] into a BI with internal equality. *) bi_embed_mixin_interal_inj `{BiInternalEq PROP'} (P Q : PROP1) : ⎡P⎤ ≡ ⎡Q⎤ ⊢@{PROP'} (P ≡ Q); bi_embed_mixin_emp_2 : emp ⊢@{PROP2} ⎡emp⎤;