Commit 1e512d6e by Ralf Jung

use type-ascribed equality notation

parent 12ac96cd
 ... ... @@ -285,18 +285,18 @@ Proof. Qed. Lemma core_singleton (i : K) (x : A) cx : pcore x = Some cx → core ({[ i := x ]} : gmap K A) = {[ i := cx ]}. pcore x = Some cx → core {[ i := x ]} =@{gmap K A} {[ i := cx ]}. Proof. apply omap_singleton. Qed. Lemma core_singleton' (i : K) (x : A) cx : pcore x ≡ Some cx → core ({[ i := x ]} : gmap K A) ≡ {[ i := cx ]}. pcore x ≡ Some cx → core {[ i := x ]} ≡@{gmap K A} {[ i := cx ]}. Proof. intros (cx'&?&->)%equiv_Some_inv_r'. by rewrite (core_singleton _ _ cx'). Qed. Lemma singleton_core_total `{!CmraTotal A} (i : K) (x : A) : core ({[ i := x ]} : gmap K A) = {[ i := core x ]}. core {[ i := x ]} =@{gmap K A} {[ i := core x ]}. Proof. apply core_singleton. rewrite cmra_pcore_core //. Qed. Lemma op_singleton (i : K) (x y : A) : {[ i := x ]} ⋅ {[ i := y ]} = ({[ i := x ⋅ y ]} : gmap K A). {[ i := x ]} ⋅ {[ i := y ]} =@{gmap K A} {[ i := x ⋅ y ]}. Proof. by apply (merge_singleton _ _ _ x y). Qed. Global Instance is_op_singleton i a a1 a2 : IsOp a a1 a2 → IsOp' ({[ i := a ]} : gmap K A) {[ i := a1 ]} {[ i := a2 ]}. ... ...
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