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<a id="++⁺"></a><a id="3585" href="Data.List.Relation.Binary.Equality.Setoid.html#3585" class="Function">++⁺</a> <a id="3589" class="Symbol">:</a> <a id="3591" href="Data.List.Relation.Binary.Equality.Setoid.html#1311" class="Generalizable">ws</a> <a id="3594" href="Data.List.Relation.Binary.Equality.Setoid.html#1555" class="Function Operator">≋</a> <a id="3596" href="Data.List.Relation.Binary.Equality.Setoid.html#1314" class="Generalizable">xs</a> <a id="3599" class="Symbol">→</a> <a id="3601" href="Data.List.Relation.Binary.Equality.Setoid.html#1321" class="Generalizable">ys</a> <a id="3604" href="Data.List.Relation.Binary.Equality.Setoid.html#1555" class="Function Operator">≋</a> <a id="3606" href="Data.List.Relation.Binary.Equality.Setoid.html#1328" class="Generalizable">zs</a> <a id="3609" class="Symbol">→</a> <a id="3611" href="Data.List.Relation.Binary.Equality.Setoid.html#1311" class="Generalizable">ws</a> <a id="3614" href="Data.List.Base.html#1734" class="Function Operator">++</a> <a id="3617" href="Data.List.Relation.Binary.Equality.Setoid.html#1321" class="Generalizable">ys</a> <a id="3620" href="Data.List.Relation.Binary.Equality.Setoid.html#1555" class="Function Operator">≋</a> <a id="3622" href="Data.List.Relation.Binary.Equality.Setoid.html#1314" class="Generalizable">xs</a> <a id="3625" href="Data.List.Base.html#1734" class="Function Operator">++</a> <a id="3628" href="Data.List.Relation.Binary.Equality.Setoid.html#1328" class="Generalizable">zs</a>
<a id="3631" href="Data.List.Relation.Binary.Equality.Setoid.html#3585" class="Function">++⁺</a> <a id="3635" class="Symbol">=</a> <a id="3637" href="Data.List.Relation.Binary.Pointwise.html#5818" class="Function">PW.++⁺</a>

<a id="++⁺ʳ"></a><a id="3645" href="Data.List.Relation.Binary.Equality.Setoid.html#3645" class="Function">++⁺ʳ</a> <a id="3650" class="Symbol">:</a> <a id="3652" class="Symbol">∀</a> <a id="3654" href="Data.List.Relation.Binary.Equality.Setoid.html#3654" class="Bound">xs</a> <a id="3657" class="Symbol">→</a> <a id="3659" href="Data.List.Relation.Binary.Equality.Setoid.html#1321" class="Generalizable">ys</a> <a id="3662" href="Data.List.Relation.Binary.Equality.Setoid.html#1555" class="Function Operator">≋</a> <a id="3664" href="Data.List.Relation.Binary.Equality.Setoid.html#1328" class="Generalizable">zs</a> <a id="3667" class="Symbol">→</a> <a id="3669" href="Data.List.Relation.Binary.Equality.Setoid.html#3654" class="Bound">xs</a> <a id="3672" href="Data.List.Base.html#1734" class="Function Operator">++</a> <a id="3675" href="Data.List.Relation.Binary.Equality.Setoid.html#1321" class="Generalizable">ys</a> <a id="3678" href="Data.List.Relation.Binary.Equality.Setoid.html#1555" class="Function Operator">≋</a> <a id="3680" href="Data.List.Relation.Binary.Equality.Setoid.html#3654" class="Bound">xs</a> <a id="3683" href="Data.List.Base.html#1734" class="Function Operator">++</a> <a id="3686" href="Data.List.Relation.Binary.Equality.Setoid.html#1328" class="Generalizable">zs</a>
<a id="3689" href="Data.List.Relation.Binary.Equality.Setoid.html#3645" class="Function">++⁺ʳ</a> <a id="3694" href="Data.List.Relation.Binary.Equality.Setoid.html#3694" class="Bound">xs</a> <a id="3697" class="Symbol">=</a> <a id="3699" href="Data.List.Relation.Binary.Pointwise.html#6736" class="Function">PW.++⁺ʳ</a> <a id="3707" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="3712" href="Data.List.Relation.Binary.Equality.Setoid.html#3694" class="Bound">xs</a>
<a id="++⁺ˡ"></a><a id="3645" href="Data.List.Relation.Binary.Equality.Setoid.html#3645" class="Function">++⁺ˡ</a> <a id="3650" class="Symbol">:</a> <a id="3652" class="Symbol">∀</a> <a id="3654" href="Data.List.Relation.Binary.Equality.Setoid.html#3654" class="Bound">xs</a> <a id="3657" class="Symbol">→</a> <a id="3659" href="Data.List.Relation.Binary.Equality.Setoid.html#1321" class="Generalizable">ys</a> <a id="3662" href="Data.List.Relation.Binary.Equality.Setoid.html#1555" class="Function Operator">≋</a> <a id="3664" href="Data.List.Relation.Binary.Equality.Setoid.html#1328" class="Generalizable">zs</a> <a id="3667" class="Symbol">→</a> <a id="3669" href="Data.List.Relation.Binary.Equality.Setoid.html#3654" class="Bound">xs</a> <a id="3672" href="Data.List.Base.html#1734" class="Function Operator">++</a> <a id="3675" href="Data.List.Relation.Binary.Equality.Setoid.html#1321" class="Generalizable">ys</a> <a id="3678" href="Data.List.Relation.Binary.Equality.Setoid.html#1555" class="Function Operator">≋</a> <a id="3680" href="Data.List.Relation.Binary.Equality.Setoid.html#3654" class="Bound">xs</a> <a id="3683" href="Data.List.Base.html#1734" class="Function Operator">++</a> <a id="3686" href="Data.List.Relation.Binary.Equality.Setoid.html#1328" class="Generalizable">zs</a>
<a id="3689" href="Data.List.Relation.Binary.Equality.Setoid.html#3645" class="Function">++⁺ˡ</a> <a id="3694" href="Data.List.Relation.Binary.Equality.Setoid.html#3694" class="Bound">xs</a> <a id="3697" class="Symbol">=</a> <a id="3699" href="Data.List.Relation.Binary.Pointwise.html#6736" class="Function">PW.++⁺ˡ</a> <a id="3707" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="3712" href="Data.List.Relation.Binary.Equality.Setoid.html#3694" class="Bound">xs</a>

<a id="++⁺ˡ"></a><a id="3716" href="Data.List.Relation.Binary.Equality.Setoid.html#3716" class="Function">++⁺ˡ</a> <a id="3721" class="Symbol">:</a> <a id="3723" class="Symbol">∀</a> <a id="3725" href="Data.List.Relation.Binary.Equality.Setoid.html#3725" class="Bound">zs</a> <a id="3728" class="Symbol">→</a> <a id="3730" href="Data.List.Relation.Binary.Equality.Setoid.html#1311" class="Generalizable">ws</a> <a id="3733" href="Data.List.Relation.Binary.Equality.Setoid.html#1555" class="Function Operator">≋</a> <a id="3735" href="Data.List.Relation.Binary.Equality.Setoid.html#1314" class="Generalizable">xs</a> <a id="3738" class="Symbol">→</a> <a id="3740" href="Data.List.Relation.Binary.Equality.Setoid.html#1311" class="Generalizable">ws</a> <a id="3743" href="Data.List.Base.html#1734" class="Function Operator">++</a> <a id="3746" href="Data.List.Relation.Binary.Equality.Setoid.html#3725" class="Bound">zs</a> <a id="3749" href="Data.List.Relation.Binary.Equality.Setoid.html#1555" class="Function Operator">≋</a> <a id="3751" href="Data.List.Relation.Binary.Equality.Setoid.html#1314" class="Generalizable">xs</a> <a id="3754" href="Data.List.Base.html#1734" class="Function Operator">++</a> <a id="3757" href="Data.List.Relation.Binary.Equality.Setoid.html#3725" class="Bound">zs</a>
<a id="3760" href="Data.List.Relation.Binary.Equality.Setoid.html#3716" class="Function">++⁺ˡ</a> <a id="3765" href="Data.List.Relation.Binary.Equality.Setoid.html#3765" class="Bound">zs</a> <a id="3768" class="Symbol">=</a> <a id="3770" href="Data.List.Relation.Binary.Pointwise.html#6829" class="Function">PW.++⁺ˡ</a> <a id="3778" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="3783" href="Data.List.Relation.Binary.Equality.Setoid.html#3765" class="Bound">zs</a>
<a id="++⁺ʳ"></a><a id="3716" href="Data.List.Relation.Binary.Equality.Setoid.html#3716" class="Function">++⁺ʳ</a> <a id="3721" class="Symbol">:</a> <a id="3723" class="Symbol">∀</a> <a id="3725" href="Data.List.Relation.Binary.Equality.Setoid.html#3725" class="Bound">zs</a> <a id="3728" class="Symbol">→</a> <a id="3730" href="Data.List.Relation.Binary.Equality.Setoid.html#1311" class="Generalizable">ws</a> <a id="3733" href="Data.List.Relation.Binary.Equality.Setoid.html#1555" class="Function Operator">≋</a> <a id="3735" href="Data.List.Relation.Binary.Equality.Setoid.html#1314" class="Generalizable">xs</a> <a id="3738" class="Symbol">→</a> <a id="3740" href="Data.List.Relation.Binary.Equality.Setoid.html#1311" class="Generalizable">ws</a> <a id="3743" href="Data.List.Base.html#1734" class="Function Operator">++</a> <a id="3746" href="Data.List.Relation.Binary.Equality.Setoid.html#3725" class="Bound">zs</a> <a id="3749" href="Data.List.Relation.Binary.Equality.Setoid.html#1555" class="Function Operator">≋</a> <a id="3751" href="Data.List.Relation.Binary.Equality.Setoid.html#1314" class="Generalizable">xs</a> <a id="3754" href="Data.List.Base.html#1734" class="Function Operator">++</a> <a id="3757" href="Data.List.Relation.Binary.Equality.Setoid.html#3725" class="Bound">zs</a>
<a id="3760" href="Data.List.Relation.Binary.Equality.Setoid.html#3716" class="Function">++⁺ʳ</a> <a id="3765" href="Data.List.Relation.Binary.Equality.Setoid.html#3765" class="Bound">zs</a> <a id="3768" class="Symbol">=</a> <a id="3770" href="Data.List.Relation.Binary.Pointwise.html#6829" class="Function">PW.++⁺ʳ</a> <a id="3778" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="3783" href="Data.List.Relation.Binary.Equality.Setoid.html#3765" class="Bound">zs</a>

<a id="++-cancelˡ"></a><a id="3787" href="Data.List.Relation.Binary.Equality.Setoid.html#3787" class="Function">++-cancelˡ</a> <a id="3798" class="Symbol">:</a> <a id="3800" class="Symbol">∀</a> <a id="3802" href="Data.List.Relation.Binary.Equality.Setoid.html#3802" class="Bound">xs</a> <a id="3805" class="Symbol">{</a><a id="3806" href="Data.List.Relation.Binary.Equality.Setoid.html#3806" class="Bound">ys</a> <a id="3809" href="Data.List.Relation.Binary.Equality.Setoid.html#3809" class="Bound">zs</a><a id="3811" class="Symbol">}</a> <a id="3813" class="Symbol">→</a> <a id="3815" href="Data.List.Relation.Binary.Equality.Setoid.html#3802" class="Bound">xs</a> <a id="3818" href="Data.List.Base.html#1734" class="Function Operator">++</a> <a id="3821" href="Data.List.Relation.Binary.Equality.Setoid.html#3806" class="Bound">ys</a> <a id="3824" href="Data.List.Relation.Binary.Equality.Setoid.html#1555" class="Function Operator">≋</a> <a id="3826" href="Data.List.Relation.Binary.Equality.Setoid.html#3802" class="Bound">xs</a> <a id="3829" href="Data.List.Base.html#1734" class="Function Operator">++</a> <a id="3832" href="Data.List.Relation.Binary.Equality.Setoid.html#3809" class="Bound">zs</a> <a id="3835" class="Symbol">→</a> <a id="3837" href="Data.List.Relation.Binary.Equality.Setoid.html#3806" class="Bound">ys</a> <a id="3840" href="Data.List.Relation.Binary.Equality.Setoid.html#1555" class="Function Operator">≋</a> <a id="3842" href="Data.List.Relation.Binary.Equality.Setoid.html#3809" class="Bound">zs</a>
<a id="3845" href="Data.List.Relation.Binary.Equality.Setoid.html#3787" class="Function">++-cancelˡ</a> <a id="3856" href="Data.List.Relation.Binary.Equality.Setoid.html#3856" class="Bound">xs</a> <a id="3859" class="Symbol">=</a> <a id="3861" href="Data.List.Relation.Binary.Pointwise.html#5985" class="Function">PW.++-cancelˡ</a> <a id="3875" href="Data.List.Relation.Binary.Equality.Setoid.html#3856" class="Bound">xs</a>
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<a id="6698" class="Keyword">module</a> <a id="6705" href="Data.List.Relation.Binary.Pointwise.html#6705" class="Module">_</a> <a id="6707" class="Symbol">(</a><a id="6708" href="Data.List.Relation.Binary.Pointwise.html#6708" class="Bound">rfl</a> <a id="6712" class="Symbol">:</a> <a id="6714" href="Relation.Binary.Definitions.html#1332" class="Function">Reflexive</a> <a id="6724" href="Data.List.Relation.Binary.Pointwise.html#1754" class="Generalizable">R</a><a id="6725" class="Symbol">)</a> <a id="6727" class="Keyword">where</a>

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<a id="6801" href="Data.List.Relation.Binary.Pointwise.html#6736" class="Function">++⁺ʳ</a> <a id="6806" href="Data.List.Relation.Binary.Pointwise.html#6806" class="Bound">xs</a> <a id="6809" class="Symbol">=</a> <a id="6811" href="Data.List.Relation.Binary.Pointwise.html#5818" class="Function">++⁺</a> <a id="6815" class="Symbol">(</a><a id="6816" href="Data.List.Relation.Binary.Pointwise.Properties.html#1079" class="Function">refl</a> <a id="6821" href="Data.List.Relation.Binary.Pointwise.html#6708" class="Bound">rfl</a><a id="6824" class="Symbol">)</a>
<a id="6736" href="Data.List.Relation.Binary.Pointwise.html#6736" class="Function">++⁺ˡ</a> <a id="6741" class="Symbol">:</a> <a id="6743" class="Symbol">∀</a> <a id="6745" href="Data.List.Relation.Binary.Pointwise.html#6745" class="Bound">xs</a> <a id="6748" class="Symbol">→</a> <a id="6750" class="Symbol">(</a><a id="6751" href="Data.List.Relation.Binary.Pointwise.html#6745" class="Bound">xs</a> <a id="6754" href="Data.List.Base.html#1734" class="Function Operator">++_</a><a id="6757" class="Symbol">)</a> <a id="6759" href="Relation.Binary.Core.html#1577" class="Function Operator">Preserves</a> <a id="6769" class="Symbol">(</a><a id="6770" href="Data.List.Relation.Binary.Pointwise.Base.html#884" class="Datatype">Pointwise</a> <a id="6780" href="Data.List.Relation.Binary.Pointwise.html#6724" class="Bound">R</a><a id="6781" class="Symbol">)</a> <a id="6783" href="Relation.Binary.Core.html#1577" class="Function Operator">⟶</a> <a id="6785" class="Symbol">(</a><a id="6786" href="Data.List.Relation.Binary.Pointwise.Base.html#884" class="Datatype">Pointwise</a> <a id="6796" href="Data.List.Relation.Binary.Pointwise.html#6724" class="Bound">R</a><a id="6797" class="Symbol">)</a>
<a id="6801" href="Data.List.Relation.Binary.Pointwise.html#6736" class="Function">++⁺ˡ</a> <a id="6806" href="Data.List.Relation.Binary.Pointwise.html#6806" class="Bound">xs</a> <a id="6809" class="Symbol">=</a> <a id="6811" href="Data.List.Relation.Binary.Pointwise.html#5818" class="Function">++⁺</a> <a id="6815" class="Symbol">(</a><a id="6816" href="Data.List.Relation.Binary.Pointwise.Properties.html#1079" class="Function">refl</a> <a id="6821" href="Data.List.Relation.Binary.Pointwise.html#6708" class="Bound">rfl</a><a id="6824" class="Symbol">)</a>

<a id="6829" href="Data.List.Relation.Binary.Pointwise.html#6829" class="Function">++⁺ˡ</a> <a id="6834" class="Symbol">:</a> <a id="6836" class="Symbol">∀</a> <a id="6838" href="Data.List.Relation.Binary.Pointwise.html#6838" class="Bound">zs</a> <a id="6841" class="Symbol">→</a> <a id="6843" class="Symbol">(</a><a id="6844" href="Data.List.Base.html#1734" class="Function Operator">_++</a> <a id="6848" href="Data.List.Relation.Binary.Pointwise.html#6838" class="Bound">zs</a><a id="6850" class="Symbol">)</a> <a id="6852" href="Relation.Binary.Core.html#1577" class="Function Operator">Preserves</a> <a id="6862" class="Symbol">(</a><a id="6863" href="Data.List.Relation.Binary.Pointwise.Base.html#884" class="Datatype">Pointwise</a> <a id="6873" href="Data.List.Relation.Binary.Pointwise.html#6724" class="Bound">R</a><a id="6874" class="Symbol">)</a> <a id="6876" href="Relation.Binary.Core.html#1577" class="Function Operator">⟶</a> <a id="6878" class="Symbol">(</a><a id="6879" href="Data.List.Relation.Binary.Pointwise.Base.html#884" class="Datatype">Pointwise</a> <a id="6889" href="Data.List.Relation.Binary.Pointwise.html#6724" class="Bound">R</a><a id="6890" class="Symbol">)</a>
<a id="6894" href="Data.List.Relation.Binary.Pointwise.html#6829" class="Function">++⁺ˡ</a> <a id="6899" href="Data.List.Relation.Binary.Pointwise.html#6899" class="Bound">zs</a> <a id="6902" href="Data.List.Relation.Binary.Pointwise.html#6902" class="Bound">rs</a> <a id="6905" class="Symbol">=</a> <a id="6907" href="Data.List.Relation.Binary.Pointwise.html#5818" class="Function">++⁺</a> <a id="6911" href="Data.List.Relation.Binary.Pointwise.html#6902" class="Bound">rs</a> <a id="6914" class="Symbol">(</a><a id="6915" href="Data.List.Relation.Binary.Pointwise.Properties.html#1079" class="Function">refl</a> <a id="6920" href="Data.List.Relation.Binary.Pointwise.html#6708" class="Bound">rfl</a><a id="6923" class="Symbol">)</a>
<a id="6829" href="Data.List.Relation.Binary.Pointwise.html#6829" class="Function">++⁺ʳ</a> <a id="6834" class="Symbol">:</a> <a id="6836" class="Symbol">∀</a> <a id="6838" href="Data.List.Relation.Binary.Pointwise.html#6838" class="Bound">zs</a> <a id="6841" class="Symbol">→</a> <a id="6843" class="Symbol">(</a><a id="6844" href="Data.List.Base.html#1734" class="Function Operator">_++</a> <a id="6848" href="Data.List.Relation.Binary.Pointwise.html#6838" class="Bound">zs</a><a id="6850" class="Symbol">)</a> <a id="6852" href="Relation.Binary.Core.html#1577" class="Function Operator">Preserves</a> <a id="6862" class="Symbol">(</a><a id="6863" href="Data.List.Relation.Binary.Pointwise.Base.html#884" class="Datatype">Pointwise</a> <a id="6873" href="Data.List.Relation.Binary.Pointwise.html#6724" class="Bound">R</a><a id="6874" class="Symbol">)</a> <a id="6876" href="Relation.Binary.Core.html#1577" class="Function Operator">⟶</a> <a id="6878" class="Symbol">(</a><a id="6879" href="Data.List.Relation.Binary.Pointwise.Base.html#884" class="Datatype">Pointwise</a> <a id="6889" href="Data.List.Relation.Binary.Pointwise.html#6724" class="Bound">R</a><a id="6890" class="Symbol">)</a>
<a id="6894" href="Data.List.Relation.Binary.Pointwise.html#6829" class="Function">++⁺ʳ</a> <a id="6899" href="Data.List.Relation.Binary.Pointwise.html#6899" class="Bound">zs</a> <a id="6902" href="Data.List.Relation.Binary.Pointwise.html#6902" class="Bound">rs</a> <a id="6905" class="Symbol">=</a> <a id="6907" href="Data.List.Relation.Binary.Pointwise.html#5818" class="Function">++⁺</a> <a id="6911" href="Data.List.Relation.Binary.Pointwise.html#6902" class="Bound">rs</a> <a id="6914" class="Symbol">(</a><a id="6915" href="Data.List.Relation.Binary.Pointwise.Properties.html#1079" class="Function">refl</a> <a id="6920" href="Data.List.Relation.Binary.Pointwise.html#6708" class="Bound">rfl</a><a id="6923" class="Symbol">)</a>


<a id="6927" class="Comment">------------------------------------------------------------------------</a>
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