patrick/agdaproofs
1
0
Fork 0
mirror of https://github.com/Smaug123/agdaproofs synced 2025-10-17 17:38:38 +00:00
Code Issues Packages Projects Releases Wiki Activity

Define the free product (#104)

Browse Source
This commit is contained in:
Patrick Stevens
2020-03-28 21:34:14 +00:00
committed by GitHub
parent 162a1c7a40
commit a27375db4e
21 changed files with 1326 additions and 18 deletions
Download Patch File Download Diff File Expand all files Collapse all files

2
Groups/Homomorphisms/Lemmas.agda
View File

@@ -32,7 +32,7 @@ GroupHom.groupHom (groupHomsCompose {U = U} {_+C_ = _·C_} {I} {g} gHom) {x} {y}
answer = (Equivalence.transitive (Setoid.eq U)) (GroupHom.wellDefined gHom (GroupHom.groupHom hom {x} {y}) ) (GroupHom.groupHom gHom {f x} {f y})
homRespectsInverse : {x : A} → Setoid._∼_ T (f (Group.inverse G x)) (Group.inverse H (f x))
homRespectsInverse {x} = rightInversesAreUnique H (f x) (f (Group.inverse G x)) (transitive (symmetric (GroupHom.groupHom hom)) (transitive (GroupHom.wellDefined hom (Group.invLeft G)) imageOfIdentityIsIdentity))
homRespectsInverse {x} = rightInversesAreUnique H {f x} {f (Group.inverse G x)} (transitive (symmetric (GroupHom.groupHom hom)) (transitive (GroupHom.wellDefined hom (Group.invLeft G)) imageOfIdentityIsIdentity))
where
open Setoid T
open Equivalence eq