22< html > < head > < meta charset ="utf-8 "> < title > Cubical.Algebra.AbGroup.Instances.DiffInt</ title > < link rel ="stylesheet " href ="Agda.css "> </ head > < body > < pre class ="Agda "> < a id ="1 " class ="Comment "> -- It is recommended to use Cubical.Algebra.CommRing.Instances.Int</ a >
33< a id ="68 " class ="Comment "> -- instead of this file.</ a >
44
5- < a id ="94 " class ="Symbol "> {-#</ a > < a id ="98 " class ="Keyword "> OPTIONS</ a > < a id ="106 " class ="Pragma "> --safe</ a > < a id ="113 " class ="Symbol "> #-}</ a >
6- < a id ="117 " class ="Keyword "> module</ a > < a id ="124 " href ="Cubical.Algebra.AbGroup.Instances.DiffInt.html " class ="Module "> Cubical.Algebra.AbGroup.Instances.DiffInt</ a > < a id ="166 " class ="Keyword "> where</ a >
5+ < a id ="94 " class ="Keyword "> module</ a > < a id ="101 " href ="Cubical.Algebra.AbGroup.Instances.DiffInt.html " class ="Module "> Cubical.Algebra.AbGroup.Instances.DiffInt</ a > < a id ="143 " class ="Keyword "> where</ a >
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8- < a id ="173 " class ="Keyword "> open</ a > < a id ="178 " class ="Keyword "> import</ a > < a id ="185 " href ="Cubical.Foundations.Prelude.html " class ="Module "> Cubical.Foundations.Prelude</ a >
9- < a id ="213 " class ="Keyword "> open</ a > < a id ="218 " class ="Keyword "> import</ a > < a id ="225 " href ="Cubical.HITs.SetQuotients.html " class ="Module "> Cubical.HITs.SetQuotients</ a >
7+ < a id ="150 " class ="Keyword "> open</ a > < a id ="155 " class ="Keyword "> import</ a > < a id ="162 " href ="Cubical.Foundations.Prelude.html " class ="Module "> Cubical.Foundations.Prelude</ a >
8+ < a id ="190 " class ="Keyword "> open</ a > < a id ="195 " class ="Keyword "> import</ a > < a id ="202 " href ="Cubical.HITs.SetQuotients.html " class ="Module "> Cubical.HITs.SetQuotients</ a >
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11- < a id ="252 " class ="Keyword "> open</ a > < a id ="257 " class ="Keyword "> import</ a > < a id ="264 " href ="Cubical.Algebra.AbGroup.Base.html " class ="Module "> Cubical.Algebra.AbGroup.Base</ a >
12- < a id ="293 " class ="Keyword "> open</ a > < a id ="298 " class ="Keyword "> import</ a > < a id ="305 " href ="Cubical.Data.Int.MoreInts.DiffInt.html " class ="Module "> Cubical.Data.Int.MoreInts.DiffInt</ a >
13- < a id ="341 " class ="Keyword "> renaming</ a > < a id ="350 " class ="Symbol "> (</ a >
14- < a id ="356 " href ="Cubical.Data.Int.MoreInts.DiffInt.Properties.html#4830 " class ="Function Operator "> _+_</ a > < a id ="360 " class ="Symbol "> to</ a > < a id ="363 " class ="Function Operator "> _+ℤ_</ a >
15- < a id ="370 " class ="Symbol "> )</ a >
10+ < a id ="229 " class ="Keyword "> open</ a > < a id ="234 " class ="Keyword "> import</ a > < a id ="241 " href ="Cubical.Algebra.AbGroup.Base.html " class ="Module "> Cubical.Algebra.AbGroup.Base</ a >
11+ < a id ="270 " class ="Keyword "> open</ a > < a id ="275 " class ="Keyword "> import</ a > < a id ="282 " href ="Cubical.Data.Int.MoreInts.DiffInt.html " class ="Module "> Cubical.Data.Int.MoreInts.DiffInt</ a >
12+ < a id ="318 " class ="Keyword "> renaming</ a > < a id ="327 " class ="Symbol "> (</ a >
13+ < a id ="333 " href ="Cubical.Data.Int.MoreInts.DiffInt.Properties.html#4807 " class ="Function Operator "> _+_</ a > < a id ="337 " class ="Symbol "> to</ a > < a id ="340 " class ="Function Operator "> _+ℤ_</ a >
14+ < a id ="347 " class ="Symbol "> )</ a >
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17- < a id ="DiffℤasAbGroup "> </ a > < a id ="373 " href ="Cubical.Algebra.AbGroup.Instances.DiffInt.html#373 " class ="Function "> DiffℤasAbGroup</ a > < a id ="388 " class ="Symbol "> :</ a > < a id ="390 " href ="Cubical.Algebra.AbGroup.Base.html#1781 " class ="Function "> AbGroup</ a > < a id ="398 " href ="Agda.Primitive.html#915 " class ="Primitive "> ℓ-zero</ a >
18- < a id ="405 " href ="Cubical.Algebra.AbGroup.Instances.DiffInt.html#373 " class ="Function "> DiffℤasAbGroup</ a > < a id ="420 " class ="Symbol "> =</ a > < a id ="422 " href ="Cubical.Algebra.AbGroup.Base.html#2711 " class ="Function "> makeAbGroup</ a > < a id ="434 " class ="Symbol "> {</ a > < a id ="435 " class ="Argument "> G</ a > < a id ="437 " class ="Symbol "> =</ a > < a id ="439 " href ="Cubical.Data.Int.MoreInts.DiffInt.Base.html#467 " class ="Function "> ℤ</ a > < a id ="440 " class ="Symbol "> }</ a >
19- < a id ="471 " href ="Cubical.HITs.SetQuotients.Base.html#289 " class ="InductiveConstructor Operator "> [</ a > < a id ="473 " class ="Symbol "> (</ a > < a id ="474 " class ="Number "> 0</ a > < a id ="476 " href ="Agda.Builtin.Sigma.html#235 " class ="InductiveConstructor Operator "> ,</ a > < a id ="478 " class ="Number "> 0</ a > < a id ="479 " class ="Symbol "> )</ a > < a id ="481 " href ="Cubical.HITs.SetQuotients.Base.html#289 " class ="InductiveConstructor Operator "> ]</ a >
20- < a id ="512 " href ="Cubical.Algebra.AbGroup.Instances.DiffInt.html#363 " class ="Function Operator "> _+ℤ_</ a >
21- < a id ="546 " href ="Cubical.Data.Int.MoreInts.DiffInt.Properties.html#6464 " class ="Function Operator "> -ℤ_</ a >
22- < a id ="579 " href ="Cubical.Data.Int.MoreInts.DiffInt.Properties.html#4777 " class ="Function "> ℤ-isSet</ a >
23- < a id ="616 " href ="Cubical.Data.Int.MoreInts.DiffInt.Properties.html#8616 " class ="Function "> +ℤ-assoc</ a >
24- < a id ="654 " class ="Symbol "> (λ</ a > < a id ="657 " href ="Cubical.Algebra.AbGroup.Instances.DiffInt.html#657 " class ="Bound "> x</ a > < a id ="659 " class ="Symbol "> →</ a > < a id ="661 " href ="Cubical.Data.Int.MoreInts.DiffInt.Properties.html#6147 " class ="Function "> zero-identityʳ</ a > < a id ="676 " class ="Number "> 0</ a > < a id ="678 " href ="Cubical.Algebra.AbGroup.Instances.DiffInt.html#657 " class ="Bound "> x</ a > < a id ="679 " class ="Symbol "> )</ a >
25- < a id ="710 " class ="Symbol "> (λ</ a > < a id ="713 " href ="Cubical.Algebra.AbGroup.Instances.DiffInt.html#713 " class ="Bound "> x</ a > < a id ="715 " class ="Symbol "> →</ a > < a id ="717 " href ="Cubical.Data.Int.MoreInts.DiffInt.Properties.html#8088 " class ="Function "> -ℤ-invʳ</ a > < a id ="725 " href ="Cubical.Algebra.AbGroup.Instances.DiffInt.html#713 " class ="Bound "> x</ a > < a id ="726 " class ="Symbol "> )</ a >
26- < a id ="757 " href ="Cubical.Data.Int.MoreInts.DiffInt.Properties.html#8793 " class ="Function "> +ℤ-comm</ a >
16+ < a id ="DiffℤasAbGroup "> </ a > < a id ="350 " href ="Cubical.Algebra.AbGroup.Instances.DiffInt.html#350 " class ="Function "> DiffℤasAbGroup</ a > < a id ="365 " class ="Symbol "> :</ a > < a id ="367 " href ="Cubical.Algebra.AbGroup.Base.html#1758 " class ="Function "> AbGroup</ a > < a id ="375 " href ="Agda.Primitive.html#915 " class ="Primitive "> ℓ-zero</ a >
17+ < a id ="382 " href ="Cubical.Algebra.AbGroup.Instances.DiffInt.html#350 " class ="Function "> DiffℤasAbGroup</ a > < a id ="397 " class ="Symbol "> =</ a > < a id ="399 " href ="Cubical.Algebra.AbGroup.Base.html#2688 " class ="Function "> makeAbGroup</ a > < a id ="411 " class ="Symbol "> {</ a > < a id ="412 " class ="Argument "> G</ a > < a id ="414 " class ="Symbol "> =</ a > < a id ="416 " href ="Cubical.Data.Int.MoreInts.DiffInt.Base.html#444 " class ="Function "> ℤ</ a > < a id ="417 " class ="Symbol "> }</ a >
18+ < a id ="448 " href ="Cubical.HITs.SetQuotients.Base.html#266 " class ="InductiveConstructor Operator "> [</ a > < a id ="450 " class ="Symbol "> (</ a > < a id ="451 " class ="Number "> 0</ a > < a id ="453 " href ="Agda.Builtin.Sigma.html#235 " class ="InductiveConstructor Operator "> ,</ a > < a id ="455 " class ="Number "> 0</ a > < a id ="456 " class ="Symbol "> )</ a > < a id ="458 " href ="Cubical.HITs.SetQuotients.Base.html#266 " class ="InductiveConstructor Operator "> ]</ a >
19+ < a id ="489 " href ="Cubical.Algebra.AbGroup.Instances.DiffInt.html#340 " class ="Function Operator "> _+ℤ_</ a >
20+ < a id ="523 " href ="Cubical.Data.Int.MoreInts.DiffInt.Properties.html#6441 " class ="Function Operator "> -ℤ_</ a >
21+ < a id ="556 " href ="Cubical.Data.Int.MoreInts.DiffInt.Properties.html#4754 " class ="Function "> ℤ-isSet</ a >
22+ < a id ="593 " href ="Cubical.Data.Int.MoreInts.DiffInt.Properties.html#8593 " class ="Function "> +ℤ-assoc</ a >
23+ < a id ="631 " class ="Symbol "> (λ</ a > < a id ="634 " href ="Cubical.Algebra.AbGroup.Instances.DiffInt.html#634 " class ="Bound "> x</ a > < a id ="636 " class ="Symbol "> →</ a > < a id ="638 " href ="Cubical.Data.Int.MoreInts.DiffInt.Properties.html#6124 " class ="Function "> zero-identityʳ</ a > < a id ="653 " class ="Number "> 0</ a > < a id ="655 " href ="Cubical.Algebra.AbGroup.Instances.DiffInt.html#634 " class ="Bound "> x</ a > < a id ="656 " class ="Symbol "> )</ a >
24+ < a id ="687 " class ="Symbol "> (λ</ a > < a id ="690 " href ="Cubical.Algebra.AbGroup.Instances.DiffInt.html#690 " class ="Bound "> x</ a > < a id ="692 " class ="Symbol "> →</ a > < a id ="694 " href ="Cubical.Data.Int.MoreInts.DiffInt.Properties.html#8065 " class ="Function "> -ℤ-invʳ</ a > < a id ="702 " href ="Cubical.Algebra.AbGroup.Instances.DiffInt.html#690 " class ="Bound "> x</ a > < a id ="703 " class ="Symbol "> )</ a >
25+ < a id ="734 " href ="Cubical.Data.Int.MoreInts.DiffInt.Properties.html#8770 " class ="Function "> +ℤ-comm</ a >
2726</ pre > </ body > </ html >
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