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+[concept.equalitycomparable]
+
+# 18 Concepts library [[concepts]](./#concepts)
+
+## 18.5 Comparison concepts [[concepts.compare]](concepts.compare#concept.equalitycomparable)
+
+### 18.5.4 Concept equality_comparable [concept.equalitycomparable]
+
+[ð](#concept:weakly-equality-comparable-with)
+
+`template<class T, class U>
+  concept [weakly-equality-comparable-with](#concept:weakly-equality-comparable-with "18.5.4 Concept equality_comparable [concept.equalitycomparable]") = // exposition only
+    requires(const remove_reference_t<T>& t,
+             const remove_reference_t<U>& u) {
+      { t == u } -> [boolean-testable](concept.booleantestable#concept:boolean-testable "18.5.2 Boolean testability [concept.booleantestable]");
+      { t != u } -> [boolean-testable](concept.booleantestable#concept:boolean-testable "18.5.2 Boolean testability [concept.booleantestable]");
+      { u == t } -> [boolean-testable](concept.booleantestable#concept:boolean-testable "18.5.2 Boolean testability [concept.booleantestable]");
+      { u != t } -> [boolean-testable](concept.booleantestable#concept:boolean-testable "18.5.2 Boolean testability [concept.booleantestable]");
+    };
+`
+
+[1](#1)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/concepts.tex#L1041)
+
+Given types T and U,
+let t and u be lvalues of typesconst remove_reference_t<T> andconst remove_reference_t<U> respectively[.](#1.sentence-1)
+
+T and U model[*weakly-equality-comparable-with*](#concept:weakly-equality-comparable-with "18.5.4 Concept equality_comparable [concept.equalitycomparable]")<T, U> only if
+
+- [(1.1)](#1.1)
+
+  t == u, u == t, t != u, and u != t have the same domain[.](#1.1.sentence-1)
+
+- [(1.2)](#1.2)
+
+  bool(u == t) == bool(t == u)[.](#1.2.sentence-1)
+
+- [(1.3)](#1.3)
+
+  bool(t != u) == !bool(t == u)[.](#1.3.sentence-1)
+
+- [(1.4)](#1.4)
+
+  bool(u != t) == bool(t != u)[.](#1.4.sentence-1)
+
+[ð](#concept:equality_comparable)
+
+`template<class T>
+  concept [equality_comparable](#concept:equality_comparable "18.5.4 Concept equality_comparable [concept.equalitycomparable]") = [weakly-equality-comparable-with](#concept:weakly-equality-comparable-with "18.5.4 Concept equality_comparable [concept.equalitycomparable]")<T, T>;
+`
+
+[2](#2)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/concepts.tex#L1063)
+
+Let a and b be objects of type T[.](#2.sentence-1)
+
+T models [equality_comparable](#concept:equality_comparable "18.5.4 Concept equality_comparable [concept.equalitycomparable]") only ifbool(a == b) is true when a is equal tob ([[concepts.equality]](concepts.equality "18.2 Equality preservation")), and false otherwise[.](#2.sentence-2)
+
+[3](#3)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/concepts.tex#L1069)
+
+[*Note [1](#note-1)*:
+
+The requirement that the expression a == b is equality-preserving
+implies that == is transitive and symmetric[.](#3.sentence-1)
+
+â *end note*]
+
+[ð](#concept:equality_comparable_with)
+
+`template<class T, class U>
+  concept [equality_comparable_with](#concept:equality_comparable_with "18.5.4 Concept equality_comparable [concept.equalitycomparable]") =
+    [equality_comparable](#concept:equality_comparable "18.5.4 Concept equality_comparable [concept.equalitycomparable]")<T> && [equality_comparable](#concept:equality_comparable "18.5.4 Concept equality_comparable [concept.equalitycomparable]")<U> &&
+    [comparison-common-type-with](concept.comparisoncommontype#concept:comparison-common-type-with "18.5.3 Comparison common types [concept.comparisoncommontype]")<T, U> &&
+    [equality_comparable](#concept:equality_comparable "18.5.4 Concept equality_comparable [concept.equalitycomparable]")<
+      common_reference_t<
+        const remove_reference_t<T>&,
+        const remove_reference_t<U>&>> &&
+    [weakly-equality-comparable-with](#concept:weakly-equality-comparable-with "18.5.4 Concept equality_comparable [concept.equalitycomparable]")<T, U>;
+`
+
+[4](#4)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/concepts.tex#L1089)
+
+Given types T and U,
+let t and t2 be lvalues
+denoting distinct equal objects of types const remove_reference_t<T> andremove_cvref_t<T>, respectively,
+let u and u2 be lvalues
+denoting distinct equal objects of types const remove_reference_t<U> andremove_cvref_t<U>, respectively, and
+let C be:common_reference_t<const remove_reference_t<T>&, const remove_reference_t<U>&>T and U model[equality_comparable_with](#concept:equality_comparable_with "18.5.4 Concept equality_comparable [concept.equalitycomparable]")<T, U> only ifbool(t == u) == bool(*CONVERT_TO_LVALUE*<C>(t2) == *CONVERT_TO_LVALUE*<C>(u2))