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stdpp
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ba69172b
Commit
ba69172b
authored
Apr 05, 2018
by
Robbert Krebbers
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Notation `≡ₚ@{A}`.
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ca6ea63a
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theories/list.v
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ba69172b
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@@ -46,6 +46,10 @@ Notation "x ≢ₚ y":= (¬x ≡ₚ y) (at level 70, no associativity) : stdpp_s
Notation "( x ≢ₚ)" := (λ y, x ≢ₚ y) (only parsing) : stdpp_scope.
Notation "(≢ₚ x )" := (λ y, y ≢ₚ x) (only parsing) : stdpp_scope.
Infix "≡ₚ@{ A }" :=
(@Permutation A) (at level 70, no associativity, only parsing) : stdpp_scope.
Notation "(≡ₚ@{ A } )" := (@Permutation A) (only parsing) : stdpp_scope.
Instance maybe_cons {A} : Maybe2 (@cons A) := λ l,
match l with x :: l => Some (x,l) | _ => None end.
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@@ -2115,7 +2119,7 @@ Section submseteq_dec.
refine (λ l1 l2, cast_if (decide (is_Some (list_remove_list l1 l2))));
abstract (rewrite list_remove_list_submseteq; tauto).
Defined.
Global Instance Permutation_dec : RelDecision (
Permutation : relation (list A)
).
Global Instance Permutation_dec : RelDecision (
≡ₚ@{A}
).
Proof.
refine (λ l1 l2, cast_if_and
(decide (length l1 = length l2)) (decide (l1 ⊆+ l2)));
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@@ -3110,8 +3114,7 @@ Section ret_join.
Lemma list_join_bind (ls : list (list A)) : mjoin ls = ls ≫= id.
Proof. by induction ls; f_equal/=. Qed.
Global Instance mjoin_Permutation:
Proper (@Permutation (list A) ==> (≡ₚ)) mjoin.
Global Instance mjoin_Permutation : Proper ((≡ₚ@{list A}) ==> (≡ₚ)) mjoin.
Proof. intros ?? E. by rewrite !list_join_bind, E. Qed.
Lemma elem_of_list_ret (x y : A) : x ∈ @mret list _ A y ↔ x = y.
Proof. apply elem_of_list_singleton. Qed.
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