Mercurial > hg > Members > kono > Proof > galois
changeset 13:e0d16960d10d
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author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
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date | Mon, 17 Aug 2020 15:12:36 +0900 |
parents | d960f2ea902f |
children | b45ebc91a8d1 |
files | Solvable.agda |
diffstat | 1 files changed, 0 insertions(+), 32 deletions(-) [+] |
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--- a/Solvable.agda Mon Aug 17 15:12:17 2020 +0900 +++ b/Solvable.agda Mon Aug 17 15:12:36 2020 +0900 @@ -95,38 +95,6 @@ mpf p (mpf q (mpf r ε)) ∎ where open EqReasoning (Algebra.Group.setoid G) -mpg : {x : Carrier } → (m : MP x ) → Carrier → Carrier -mpg {x} (am x) y = y ∙ x -mpg (m o m₁) y = mpf m₁ ( mpf m y ) - -mp-flatten-g : {x : Carrier } → (m : MP x ) → Carrier -mp-flatten-g {x} m = mpg {x} m ε - -∙-flatten-g : {x : Carrier } → (m : MP x ) → x ≈ mp-flatten-g m -∙-flatten-g {x} (am x) = gsym (proj₁ identity _) -∙-flatten-g {_} (am x o q) = {!!} -- ∙-cong ( ∙-flatten-g q ) grefl -∙-flatten-g (_o_ {_} {z} (_o_ {x} {y} p q) r) = lemma9 _ _ _ {!!} ( ∙-flatten-g {z} r ) where - mp-cong : {p q r : Carrier} → (P : MP p) → q ≈ r → mpg P q ≈ mpg P r - mp-cong (am x) q=r = {!!} -- ∙-cong grefl q=r - mp-cong (P o P₁) q=r = {!!} -- mp-cong P ( mp-cong P₁ q=r ) - mp-assoc : {p q r : Carrier} → (P : MP p) → mpg P q ∙ r ≈ mpg P (q ∙ r ) - mp-assoc (am x) = {!!} -- assoc _ _ _ - mp-assoc {p} {q} {r} (P o P₁) = begin - {!!} ≈⟨ {!!} ⟩ - {!!} - ∎ where open EqReasoning (Algebra.Group.setoid G) - lemma9 : (x y z : Carrier) → x ∙ y ≈ mpg p (mpg q ε) → z ≈ mpg r ε → x ∙ y ∙ z ≈ mp-flatten-g ((p o q) o r) - lemma9 x y z t s = begin - {!!} ≈⟨ {!!} ⟩ - {!!} - ∎ where open EqReasoning (Algebra.Group.setoid G) - -tet1 : (f g : Carrier ) → {!!} -tet1 f g = mp-flatten-g ((am (g ⁻¹) o am (f ⁻¹) ) o ( (am f o am g) o am ((f ∙ g) ⁻¹ ))) - -tet2 : (f g : Carrier ) → {!!} -tet2 f g = mp-flatten ((am (g ⁻¹) o am (f ⁻¹) ) o ( (am f o am g) o am ((f ∙ g) ⁻¹ ))) - lemma5 : (f g : Carrier ) → g ⁻¹ ∙ f ⁻¹ ≈ (f ∙ g) ⁻¹ lemma5 f g = begin g ⁻¹ ∙ f ⁻¹ ≈⟨ gsym (proj₂ identity _) ⟩