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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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42
Groups/LectureNotes/Lecture1.agda
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@@ -25,8 +25,8 @@ module Groups.LectureNotes.Lecture1 where
-- TODO: R is a group with +
integersMinusNotGroup : Group (reflSetoid ℤ) (_-Z_) → False
integersMinusNotGroup record { wellDefined = wellDefined ; identity = identity ; inverse = inverse ; multAssoc = multAssoc ; multIdentRight = multIdentRight ; multIdentLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } with multAssoc {nonneg 3} {nonneg 2} {nonneg 1}
integersMinusNotGroup record { wellDefined = wellDefined ; identity = identity ; inverse = inverse ; multAssoc = multAssoc ; multIdentRight = multIdentRight ; multIdentLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } | ()
integersMinusNotGroup record { +WellDefined = wellDefined ; 0G = identity ; inverse = inverse ; +Associative = multAssoc ; identRight = multIdentRight ; identLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } with multAssoc {nonneg 3} {nonneg 2} {nonneg 1}
integersMinusNotGroup record { +WellDefined = wellDefined ; 0G = identity ; inverse = inverse ; +Associative = multAssoc ; identRight = multIdentRight ; identLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } | ()
negSuccInjective : {a b : ℕ} → (negSucc a ≡ negSucc b) → a ≡ b
negSuccInjective {a} {.a} refl = refl
@@ -35,17 +35,17 @@ module Groups.LectureNotes.Lecture1 where
nonnegInjective {a} {.a} refl = refl
integersTimesNotGroup : Group (reflSetoid ℤ) (_*Z_) → False
integersTimesNotGroup record { wellDefined = wellDefined ; identity = (nonneg zero) ; inverse = inverse ; multAssoc = multAssoc ; multIdentRight = multIdentRight ; multIdentLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } with multIdentLeft {negSucc 1}
integersTimesNotGroup record { +WellDefined = wellDefined ; 0G = (nonneg zero) ; inverse = inverse ; +Associative = multAssoc ; identRight = multIdentRight ; identLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } with multIdentLeft {negSucc 1}
... | ()
integersTimesNotGroup record { wellDefined = wellDefined ; identity = (nonneg (succ zero)) ; inverse = inverse ; multAssoc = multAssoc ; multIdentRight = multIdentRight ; multIdentLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } with invLeft {nonneg zero}
integersTimesNotGroup record { +WellDefined = wellDefined ; 0G = (nonneg (succ zero)) ; inverse = inverse ; +Associative = multAssoc ; identRight = multIdentRight ; identLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } with invLeft {nonneg zero}
... | bl with inverse (nonneg zero)
integersTimesNotGroup record { wellDefined = wellDefined ; identity = (nonneg (succ zero)) ; inverse = inverse ; multAssoc = multAssoc ; multIdentRight = multIdentRight ; multIdentLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } | () | nonneg zero
integersTimesNotGroup record { wellDefined = wellDefined ; identity = (nonneg (succ zero)) ; inverse = inverse ; multAssoc = multAssoc ; multIdentRight = multIdentRight ; multIdentLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } | p | nonneg (succ x) = naughtE (nonnegInjective (transitivity (applyEquality nonneg (equalityCommutative (Semiring.productZeroRight ℕSemiring x))) p))
integersTimesNotGroup record { wellDefined = wellDefined ; identity = (nonneg (succ zero)) ; inverse = inverse ; multAssoc = multAssoc ; multIdentRight = multIdentRight ; multIdentLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } | () | negSucc x
integersTimesNotGroup record { wellDefined = wellDefined ; identity = (nonneg (succ (succ x))) ; inverse = inverse ; multAssoc = multAssoc ; multIdentRight = multIdentRight ; multIdentLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } with succInjective (negSuccInjective (multIdentLeft {negSucc 1}))
integersTimesNotGroup record { +WellDefined = wellDefined ; 0G = (nonneg (succ zero)) ; inverse = inverse ; +Associative = multAssoc ; identRight = multIdentRight ; identLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } | () | nonneg zero
integersTimesNotGroup record { +WellDefined = wellDefined ; 0G = (nonneg (succ zero)) ; inverse = inverse ; +Associative = multAssoc ; identRight = multIdentRight ; identLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } | p | nonneg (succ x) = naughtE (nonnegInjective (transitivity (applyEquality nonneg (equalityCommutative (Semiring.productZeroRight ℕSemiring x))) p))
integersTimesNotGroup record { +WellDefined = wellDefined ; 0G = (nonneg (succ zero)) ; inverse = inverse ; +Associative = multAssoc ; identRight = multIdentRight ; identLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } | () | negSucc x
integersTimesNotGroup record { +WellDefined = wellDefined ; 0G = (nonneg (succ (succ x))) ; inverse = inverse ; +Associative = multAssoc ; identRight = multIdentRight ; identLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } with succInjective (negSuccInjective (multIdentLeft {negSucc 1}))
... | ()
integersTimesNotGroup record { wellDefined = wellDefined ; identity = (negSucc x) ; inverse = inverse ; multAssoc = multAssoc ; multIdentRight = multIdentRight ; multIdentLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } with multIdentLeft {nonneg 2}
integersTimesNotGroup record { wellDefined = wellDefined ; identity = (negSucc x) ; inverse = inverse ; multAssoc = multAssoc ; multIdentRight = multIdentRight ; multIdentLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } | ()
integersTimesNotGroup record { +WellDefined = wellDefined ; 0G = (negSucc x) ; inverse = inverse ; +Associative = multAssoc ; identRight = multIdentRight ; identLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } with multIdentLeft {nonneg 2}
integersTimesNotGroup record { +WellDefined = wellDefined ; 0G = (negSucc x) ; inverse = inverse ; +Associative = multAssoc ; identRight = multIdentRight ; identLeft = multIdentLeft ; invLeft = invLeft ; invRight = invRight } | ()
-- TODO: Q is not a group with *Q
-- TODO: Q without 0 is a group with *Q
@@ -119,18 +119,18 @@ module Groups.LectureNotes.Lecture1 where
+WAssoc {c} {c} {c} = refl
weirdGroup : Group (reflSetoid Weird) _+W_
Group.wellDefined weirdGroup = reflGroupWellDefined
Group.identity weirdGroup = e
Group.+WellDefined weirdGroup = reflGroupWellDefined
Group.0G weirdGroup = e
Group.inverse weirdGroup t = t
Group.multAssoc weirdGroup {r} {s} {t} = +WAssoc {r} {s} {t}
Group.multIdentRight weirdGroup {e} = refl
Group.multIdentRight weirdGroup {a} = refl
Group.multIdentRight weirdGroup {b} = refl
Group.multIdentRight weirdGroup {c} = refl
Group.multIdentLeft weirdGroup {e} = refl
Group.multIdentLeft weirdGroup {a} = refl
Group.multIdentLeft weirdGroup {b} = refl
Group.multIdentLeft weirdGroup {c} = refl
Group.+Associative weirdGroup {r} {s} {t} = +WAssoc {r} {s} {t}
Group.identRight weirdGroup {e} = refl
Group.identRight weirdGroup {a} = refl
Group.identRight weirdGroup {b} = refl
Group.identRight weirdGroup {c} = refl
Group.identLeft weirdGroup {e} = refl
Group.identLeft weirdGroup {a} = refl
Group.identLeft weirdGroup {b} = refl
Group.identLeft weirdGroup {c} = refl
Group.invLeft weirdGroup {e} = refl
Group.invLeft weirdGroup {a} = refl
Group.invLeft weirdGroup {b} = refl