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Rename some confusing fields (#51)

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This commit is contained in:
Patrick Stevens
2019-10-13 09:31:54 +01:00
committed by GitHub
parent 96d15c6017
commit 959071214e
21 changed files with 441 additions and 441 deletions
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14
Groups/Definition.agda
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@@ -12,11 +12,11 @@ module Groups.Definition where
record Group {lvl1 lvl2} {A : Set lvl1} (S : Setoid {lvl1} {lvl2} A) (_·_ : A → A → A) : Set (lsuc lvl1 ⊔ lvl2) where
open Setoid S
field
wellDefined : {m n x y : A} → (m ∼ x) → (n ∼ y) → (m · n) ∼ (x · y)
identity : A
+WellDefined : {m n x y : A} → (m ∼ x) → (n ∼ y) → (m · n) ∼ (x · y)
0G : A
inverse : A → A
multAssoc : {a b c : A} → (a · (b · c)) ∼ (a · b) · c
multIdentRight : {a : A} → (a · identity) ∼ a
multIdentLeft : {a : A} → (identity · a) ∼ a
invLeft : {a : A} → (inverse a) · a ∼ identity
invRight : {a : A} → a · (inverse a) ∼ identity
+Associative : {a b c : A} → (a · (b · c)) ∼ (a · b) · c
identRight : {a : A} → (a · 0G) ∼ a
identLeft : {a : A} → (0G · a) ∼ a
invLeft : {a : A} → (inverse a) · a ∼ 0G
invRight : {a : A} → a · (inverse a) ∼ 0G