Datasets:
internlm
/
Lean-Github

Dataset card Data Studio Files Community
1
url
stringclasses
147 values
commit
stringclasses
147 values
file_path
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7
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stringlengths
1
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stringlengths
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2.09M
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/FieldTheory/PerfectClosure.lean
ECTate.PerfectRing.pth_root_zero
[46, 1]
[58, 76]
rw [pth_root]
R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R ⊢ pth_root 0 = 0
R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R ⊢ dite (ringChar R = 0) (fun h => id) (fun h => Function.surjInv (_ : Function.Surjective fun x => x ^ ringChar R)) 0 = 0
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/FieldTheory/PerfectClosure.lean
ECTate.PerfectRing.pth_root_zero
[46, 1]
[58, 76]
split
R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R ⊢ dite (ringChar R = 0) (fun h => id) (fun h => Function.surjInv (_ : Function.Surjective fun x => x ^ ringChar R)) 0 = 0
case inl R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ringChar R = 0 ⊢ id 0 = 0 case inr R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ¬ringChar R = 0 ⊢ Function.surjInv (_ : Function.Surjective fun x => x ^ ringChar R) 0 = 0
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/FieldTheory/PerfectClosure.lean
ECTate.PerfectRing.pth_root_zero
[46, 1]
[58, 76]
. simp
case inl R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ringChar R = 0 ⊢ id 0 = 0 case inr R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ¬ringChar R = 0 ⊢ Function.surjInv (_ : Function.Surjective fun x => x ^ ringChar R) 0 = 0
case inr R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ¬ringChar R = 0 ⊢ Function.surjInv (_ : Function.Surjective fun x => x ^ ringChar R) 0 = 0
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/FieldTheory/PerfectClosure.lean
ECTate.PerfectRing.pth_root_zero
[46, 1]
[58, 76]
. apply_fun (fun x : R => x ^ ringChar R) . simp only [ne_eq] rw [Function.surjInv_eq (pth_power_bijective_of_char_nonzero (by assumption)).surjective, zero_pow] rwa [zero_lt_iff] . exact (pth_power_bijective_of_char_nonzero (by assumption)).injective
case inr R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ¬ringChar R = 0 ⊢ Function.surjInv (_ : Function.Surjective fun x => x ^ ringChar R) 0 = 0
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/FieldTheory/PerfectClosure.lean
ECTate.PerfectRing.pth_root_zero
[46, 1]
[58, 76]
simp
case inl R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ringChar R = 0 ⊢ id 0 = 0
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/FieldTheory/PerfectClosure.lean
ECTate.PerfectRing.pth_root_zero
[46, 1]
[58, 76]
apply_fun (fun x : R => x ^ ringChar R)
case inr R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ¬ringChar R = 0 ⊢ Function.surjInv (_ : Function.Surjective fun x => x ^ ringChar R) 0 = 0
case inr R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ¬ringChar R = 0 ⊢ (fun x => x ^ ringChar R) (Function.surjInv (_ : Function.Surjective fun x => x ^ ringChar R) 0) = (fun x => x ^ ringChar R) 0 case inr.inj R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ¬ringChar R = 0 ⊢ Function.Injective fun x => x ^ ringChar R
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/FieldTheory/PerfectClosure.lean
ECTate.PerfectRing.pth_root_zero
[46, 1]
[58, 76]
. simp only [ne_eq] rw [Function.surjInv_eq (pth_power_bijective_of_char_nonzero (by assumption)).surjective, zero_pow] rwa [zero_lt_iff]
case inr R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ¬ringChar R = 0 ⊢ (fun x => x ^ ringChar R) (Function.surjInv (_ : Function.Surjective fun x => x ^ ringChar R) 0) = (fun x => x ^ ringChar R) 0 case inr.inj R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ¬ringChar R = 0 ⊢ Function.Injective fun x => x ^ ringChar R
case inr.inj R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ¬ringChar R = 0 ⊢ Function.Injective fun x => x ^ ringChar R
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/FieldTheory/PerfectClosure.lean
ECTate.PerfectRing.pth_root_zero
[46, 1]
[58, 76]
. exact (pth_power_bijective_of_char_nonzero (by assumption)).injective
case inr.inj R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ¬ringChar R = 0 ⊢ Function.Injective fun x => x ^ ringChar R
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/FieldTheory/PerfectClosure.lean
ECTate.PerfectRing.pth_root_zero
[46, 1]
[58, 76]
simp only [ne_eq]
case inr R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ¬ringChar R = 0 ⊢ (fun x => x ^ ringChar R) (Function.surjInv (_ : Function.Surjective fun x => x ^ ringChar R) 0) = (fun x => x ^ ringChar R) 0
case inr R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ¬ringChar R = 0 ⊢ Function.surjInv (_ : Function.Surjective fun x => x ^ ringChar R) 0 ^ ringChar R = 0 ^ ringChar R
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/FieldTheory/PerfectClosure.lean
ECTate.PerfectRing.pth_root_zero
[46, 1]
[58, 76]
rw [Function.surjInv_eq (pth_power_bijective_of_char_nonzero (by assumption)).surjective, zero_pow]
case inr R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ¬ringChar R = 0 ⊢ Function.surjInv (_ : Function.Surjective fun x => x ^ ringChar R) 0 ^ ringChar R = 0 ^ ringChar R
case inr R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ¬ringChar R = 0 ⊢ 0 < ringChar R
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/FieldTheory/PerfectClosure.lean
ECTate.PerfectRing.pth_root_zero
[46, 1]
[58, 76]
rwa [zero_lt_iff]
case inr R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ¬ringChar R = 0 ⊢ 0 < ringChar R
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/FieldTheory/PerfectClosure.lean
ECTate.PerfectRing.pth_root_zero
[46, 1]
[58, 76]
assumption
R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ¬ringChar R = 0 ⊢ ringChar R ≠ 0
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/FieldTheory/PerfectClosure.lean
ECTate.PerfectRing.pth_root_zero
[46, 1]
[58, 76]
exact (pth_power_bijective_of_char_nonzero (by assumption)).injective
case inr.inj R : Type u_1 inst✝¹ : CommSemiring R inst✝ : PerfectRing R h✝ : ¬ringChar R = 0 ⊢ Function.Injective fun x => x ^ ringChar R
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.b8_identity
[48, 1]
[51, 7]
simp only [b2, b4, b6, b8]
R : Type u inst✝ : CommRing R e : Model R ⊢ 4 * b8 e = b2 e * b6 e - b4 e ^ 2
R : Type u inst✝ : CommRing R e : Model R ⊢ 4 * (e.a1 * e.a1 * e.a6 - e.a1 * e.a3 * e.a4 + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 - e.a4 * e.a4) = (e.a1 * e.a1 + 4 * e.a2) * (e.a3 * e.a3 + 4 * e.a6) - (e.a1 * e.a3 + 2 * e.a4) ^ 2
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.b8_identity
[48, 1]
[51, 7]
ring
R : Type u inst✝ : CommRing R e : Model R ⊢ 4 * (e.a1 * e.a1 * e.a6 - e.a1 * e.a3 * e.a4 + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 - e.a4 * e.a4) = (e.a1 * e.a1 + 4 * e.a2) * (e.a3 * e.a3 + 4 * e.a6) - (e.a1 * e.a3 + 2 * e.a4) ^ 2
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.discr_identity
[60, 1]
[65, 7]
simp only [c4, c6, discr, mul_sub, mul_add]
R : Type u inst✝ : CommRing R e : Model R ⊢ 1728 * discr e = c4 e ^ 3 - c6 e ^ 2
R : Type u inst✝ : CommRing R e : Model R ⊢ 1728 * (-b2 e * b2 e * b8 e) - 1728 * (8 * b4 e ^ 3) - 1728 * (27 * b6 e * b6 e) + 1728 * (9 * b2 e * b4 e * b6 e) = (b2 e ^ 2 - 24 * b4 e) ^ 3 - (-b2 e ^ 3 + 36 * b2 e * b4 e - 216 * b6 e) ^ 2
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.discr_identity
[60, 1]
[65, 7]
rw [(by ring : 1728 * (-e.b2 * e.b2 * e.b8) = -432 * e.b2 * e.b2 * (4 * e.b8))]
R : Type u inst✝ : CommRing R e : Model R ⊢ 1728 * (-b2 e * b2 e * b8 e) - 1728 * (8 * b4 e ^ 3) - 1728 * (27 * b6 e * b6 e) + 1728 * (9 * b2 e * b4 e * b6 e) = (b2 e ^ 2 - 24 * b4 e) ^ 3 - (-b2 e ^ 3 + 36 * b2 e * b4 e - 216 * b6 e) ^ 2
R : Type u inst✝ : CommRing R e : Model R ⊢ -432 * b2 e * b2 e * (4 * b8 e) - 1728 * (8 * b4 e ^ 3) - 1728 * (27 * b6 e * b6 e) + 1728 * (9 * b2 e * b4 e * b6 e) = (b2 e ^ 2 - 24 * b4 e) ^ 3 - (-b2 e ^ 3 + 36 * b2 e * b4 e - 216 * b6 e) ^ 2
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.discr_identity
[60, 1]
[65, 7]
rw [b8_identity]
R : Type u inst✝ : CommRing R e : Model R ⊢ -432 * b2 e * b2 e * (4 * b8 e) - 1728 * (8 * b4 e ^ 3) - 1728 * (27 * b6 e * b6 e) + 1728 * (9 * b2 e * b4 e * b6 e) = (b2 e ^ 2 - 24 * b4 e) ^ 3 - (-b2 e ^ 3 + 36 * b2 e * b4 e - 216 * b6 e) ^ 2
R : Type u inst✝ : CommRing R e : Model R ⊢ -432 * b2 e * b2 e * (b2 e * b6 e - b4 e ^ 2) - 1728 * (8 * b4 e ^ 3) - 1728 * (27 * b6 e * b6 e) + 1728 * (9 * b2 e * b4 e * b6 e) = (b2 e ^ 2 - 24 * b4 e) ^ 3 - (-b2 e ^ 3 + 36 * b2 e * b4 e - 216 * b6 e) ^ 2
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.discr_identity
[60, 1]
[65, 7]
ring
R : Type u inst✝ : CommRing R e : Model R ⊢ -432 * b2 e * b2 e * (b2 e * b6 e - b4 e ^ 2) - 1728 * (8 * b4 e ^ 3) - 1728 * (27 * b6 e * b6 e) + 1728 * (9 * b2 e * b4 e * b6 e) = (b2 e ^ 2 - 24 * b4 e) ^ 3 - (-b2 e ^ 3 + 36 * b2 e * b4 e - 216 * b6 e) ^ 2
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.discr_identity
[60, 1]
[65, 7]
ring
R : Type u inst✝ : CommRing R e : Model R ⊢ 1728 * (-b2 e * b2 e * b8 e) = -432 * b2 e * b2 e * (4 * b8 e)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.rst_b2
[125, 1]
[127, 7]
simp [rst_iso, b2]
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ b2 (rst_iso r s t e) = b2 e + 12 * r
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ (e.a1 + 2 * s) * (e.a1 + 2 * s) + 4 * (e.a2 - s * e.a1 + 3 * r - s * s) = e.a1 * e.a1 + 4 * e.a2 + 12 * r
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.rst_b2
[125, 1]
[127, 7]
ring
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ (e.a1 + 2 * s) * (e.a1 + 2 * s) + 4 * (e.a2 - s * e.a1 + 3 * r - s * s) = e.a1 * e.a1 + 4 * e.a2 + 12 * r
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.rst_b4
[129, 1]
[133, 7]
simp only [rst_iso, b2, b4]
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ b4 (rst_iso r s t e) = b4 e + r * (b2 e + 6 * r)
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ (e.a1 + 2 * s) * (e.a3 + r * e.a1 + 2 * t) + 2 * (e.a4 - s * e.a3 + 2 * r * e.a2 - (t + r * s) * e.a1 + 3 * r * r - 2 * s * t) = e.a1 * e.a3 + 2 * e.a4 + r * (e.a1 * e.a1 + 4 * e.a2 + 6 * r)
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.rst_b4
[129, 1]
[133, 7]
ring
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ (e.a1 + 2 * s) * (e.a3 + r * e.a1 + 2 * t) + 2 * (e.a4 - s * e.a3 + 2 * r * e.a2 - (t + r * s) * e.a1 + 3 * r * r - 2 * s * t) = e.a1 * e.a3 + 2 * e.a4 + r * (e.a1 * e.a1 + 4 * e.a2 + 6 * r)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.rst_b6
[135, 1]
[139, 7]
simp only [rst_iso, b2, b4, b6]
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ b6 (rst_iso r s t e) = b6 e + 2 * r * b4 e + r * r * b2 e + 4 * r * r * r
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ (e.a3 + r * e.a1 + 2 * t) * (e.a3 + r * e.a1 + 2 * t) + 4 * (e.a6 + r * e.a4 + r * r * e.a2 + r * r * r - t * (e.a3 + t + r * e.a1)) = e.a3 * e.a3 + 4 * e.a6 + 2 * r * (e.a1 * e.a3 + 2 * e.a4) + r * r * (e.a1 * e.a1 + 4 * e.a2) + 4 * r * r * r
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.rst_b6
[135, 1]
[139, 7]
ring
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ (e.a3 + r * e.a1 + 2 * t) * (e.a3 + r * e.a1 + 2 * t) + 4 * (e.a6 + r * e.a4 + r * r * e.a2 + r * r * r - t * (e.a3 + t + r * e.a1)) = e.a3 * e.a3 + 4 * e.a6 + 2 * r * (e.a1 * e.a3 + 2 * e.a4) + r * r * (e.a1 * e.a1 + 4 * e.a2) + 4 * r * r * r
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.rst_b8
[141, 1]
[145, 7]
simp only [rst_iso, b2, b4, b6, b8]
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ b8 (rst_iso r s t e) = b8 e + 3 * r * b6 e + 3 * r * r * b4 e + r * r * r * b2 e + 3 * r * r * r * r
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ (e.a1 + 2 * s) * (e.a1 + 2 * s) * (e.a6 + r * e.a4 + r * r * e.a2 + r * r * r - t * (e.a3 + t + r * e.a1)) - (e.a1 + 2 * s) * (e.a3 + r * e.a1 + 2 * t) * (e.a4 - s * e.a3 + 2 * r * e.a2 - (t + r * s) * e.a1 + 3 * r * r - 2 * s * t) + 4 * (e.a2 - s * e.a1 + 3 * r - s * s) * (e.a6 + r * e.a4 + r * r * e.a2 + r * r * r - t * (e.a3 + t + r * e.a1)) + (e.a2 - s * e.a1 + 3 * r - s * s) * (e.a3 + r * e.a1 + 2 * t) * (e.a3 + r * e.a1 + 2 * t) - (e.a4 - s * e.a3 + 2 * r * e.a2 - (t + r * s) * e.a1 + 3 * r * r - 2 * s * t) * (e.a4 - s * e.a3 + 2 * r * e.a2 - (t + r * s) * e.a1 + 3 * r * r - 2 * s * t) = e.a1 * e.a1 * e.a6 - e.a1 * e.a3 * e.a4 + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 - e.a4 * e.a4 + 3 * r * (e.a3 * e.a3 + 4 * e.a6) + 3 * r * r * (e.a1 * e.a3 + 2 * e.a4) + r * r * r * (e.a1 * e.a1 + 4 * e.a2) + 3 * r * r * r * r
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.rst_b8
[141, 1]
[145, 7]
ring
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ (e.a1 + 2 * s) * (e.a1 + 2 * s) * (e.a6 + r * e.a4 + r * r * e.a2 + r * r * r - t * (e.a3 + t + r * e.a1)) - (e.a1 + 2 * s) * (e.a3 + r * e.a1 + 2 * t) * (e.a4 - s * e.a3 + 2 * r * e.a2 - (t + r * s) * e.a1 + 3 * r * r - 2 * s * t) + 4 * (e.a2 - s * e.a1 + 3 * r - s * s) * (e.a6 + r * e.a4 + r * r * e.a2 + r * r * r - t * (e.a3 + t + r * e.a1)) + (e.a2 - s * e.a1 + 3 * r - s * s) * (e.a3 + r * e.a1 + 2 * t) * (e.a3 + r * e.a1 + 2 * t) - (e.a4 - s * e.a3 + 2 * r * e.a2 - (t + r * s) * e.a1 + 3 * r * r - 2 * s * t) * (e.a4 - s * e.a3 + 2 * r * e.a2 - (t + r * s) * e.a1 + 3 * r * r - 2 * s * t) = e.a1 * e.a1 * e.a6 - e.a1 * e.a3 * e.a4 + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 - e.a4 * e.a4 + 3 * r * (e.a3 * e.a3 + 4 * e.a6) + 3 * r * r * (e.a1 * e.a3 + 2 * e.a4) + r * r * r * (e.a1 * e.a1 + 4 * e.a2) + 3 * r * r * r * r
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.rst_c4
[147, 1]
[152, 7]
simp only [rst_iso, b2, b4, b6, b8, c4]
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ c4 (rst_iso r s t e) = c4 e
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ ((e.a1 + 2 * s) * (e.a1 + 2 * s) + 4 * (e.a2 - s * e.a1 + 3 * r - s * s)) ^ 2 - 24 * ((e.a1 + 2 * s) * (e.a3 + r * e.a1 + 2 * t) + 2 * (e.a4 - s * e.a3 + 2 * r * e.a2 - (t + r * s) * e.a1 + 3 * r * r - 2 * s * t)) = (e.a1 * e.a1 + 4 * e.a2) ^ 2 - 24 * (e.a1 * e.a3 + 2 * e.a4)
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.rst_c4
[147, 1]
[152, 7]
ring
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ ((e.a1 + 2 * s) * (e.a1 + 2 * s) + 4 * (e.a2 - s * e.a1 + 3 * r - s * s)) ^ 2 - 24 * ((e.a1 + 2 * s) * (e.a3 + r * e.a1 + 2 * t) + 2 * (e.a4 - s * e.a3 + 2 * r * e.a2 - (t + r * s) * e.a1 + 3 * r * r - 2 * s * t)) = (e.a1 * e.a1 + 4 * e.a2) ^ 2 - 24 * (e.a1 * e.a3 + 2 * e.a4)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.rst_c6
[154, 1]
[159, 7]
simp only [rst_iso, b2, b4, b6, b8, c6]
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ c6 (rst_iso r s t e) = c6 e
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ -((e.a1 + 2 * s) * (e.a1 + 2 * s) + 4 * (e.a2 - s * e.a1 + 3 * r - s * s)) ^ 3 + 36 * ((e.a1 + 2 * s) * (e.a1 + 2 * s) + 4 * (e.a2 - s * e.a1 + 3 * r - s * s)) * ((e.a1 + 2 * s) * (e.a3 + r * e.a1 + 2 * t) + 2 * (e.a4 - s * e.a3 + 2 * r * e.a2 - (t + r * s) * e.a1 + 3 * r * r - 2 * s * t)) - 216 * ((e.a3 + r * e.a1 + 2 * t) * (e.a3 + r * e.a1 + 2 * t) + 4 * (e.a6 + r * e.a4 + r * r * e.a2 + r * r * r - t * (e.a3 + t + r * e.a1))) = -(e.a1 * e.a1 + 4 * e.a2) ^ 3 + 36 * (e.a1 * e.a1 + 4 * e.a2) * (e.a1 * e.a3 + 2 * e.a4) - 216 * (e.a3 * e.a3 + 4 * e.a6)
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.rst_c6
[154, 1]
[159, 7]
ring
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ -((e.a1 + 2 * s) * (e.a1 + 2 * s) + 4 * (e.a2 - s * e.a1 + 3 * r - s * s)) ^ 3 + 36 * ((e.a1 + 2 * s) * (e.a1 + 2 * s) + 4 * (e.a2 - s * e.a1 + 3 * r - s * s)) * ((e.a1 + 2 * s) * (e.a3 + r * e.a1 + 2 * t) + 2 * (e.a4 - s * e.a3 + 2 * r * e.a2 - (t + r * s) * e.a1 + 3 * r * r - 2 * s * t)) - 216 * ((e.a3 + r * e.a1 + 2 * t) * (e.a3 + r * e.a1 + 2 * t) + 4 * (e.a6 + r * e.a4 + r * r * e.a2 + r * r * r - t * (e.a3 + t + r * e.a1))) = -(e.a1 * e.a1 + 4 * e.a2) ^ 3 + 36 * (e.a1 * e.a1 + 4 * e.a2) * (e.a1 * e.a3 + 2 * e.a4) - 216 * (e.a3 * e.a3 + 4 * e.a6)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.rst_discr
[161, 1]
[167, 7]
simp only [discr, rst_b2, rst_b4, rst_b6, rst_b8]
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ discr (rst_iso r s t e) = discr e
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ -(b2 e + 12 * r) * (b2 e + 12 * r) * (b8 e + 3 * r * b6 e + 3 * r * r * b4 e + r * r * r * b2 e + 3 * r * r * r * r) - 8 * (b4 e + r * (b2 e + 6 * r)) ^ 3 - 27 * (b6 e + 2 * r * b4 e + r * r * b2 e + 4 * r * r * r) * (b6 e + 2 * r * b4 e + r * r * b2 e + 4 * r * r * r) + 9 * (b2 e + 12 * r) * (b4 e + r * (b2 e + 6 * r)) * (b6 e + 2 * r * b4 e + r * r * b2 e + 4 * r * r * r) = -b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e + 9 * b2 e * b4 e * b6 e
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.rst_discr
[161, 1]
[167, 7]
simp only [mul_add]
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ -(b2 e + 12 * r) * (b2 e + 12 * r) * (b8 e + 3 * r * b6 e + 3 * r * r * b4 e + r * r * r * b2 e + 3 * r * r * r * r) - 8 * (b4 e + r * (b2 e + 6 * r)) ^ 3 - 27 * (b6 e + 2 * r * b4 e + r * r * b2 e + 4 * r * r * r) * (b6 e + 2 * r * b4 e + r * r * b2 e + 4 * r * r * r) + 9 * (b2 e + 12 * r) * (b4 e + r * (b2 e + 6 * r)) * (b6 e + 2 * r * b4 e + r * r * b2 e + 4 * r * r * r) = -b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e + 9 * b2 e * b4 e * b6 e
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * b8 e + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (3 * r * b6 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (3 * r * r * b4 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (r * r * r * b2 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (3 * r * r * r * r) - 8 * (b4 e + (r * b2 e + r * (6 * r))) ^ 3 - ((27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * b6 e + (27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * (2 * r * b4 e) + (27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * (r * r * b2 e) + (27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * (4 * r * r * r)) + (((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * b6 e + ((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * (2 * r * b4 e) + ((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * (r * r * b2 e) + ((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * (4 * r * r * r)) = -b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e + 9 * b2 e * b4 e * b6 e
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.rst_discr
[161, 1]
[167, 7]
rw [(by ring : (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * b8 e = -(b2 e ^ 2 * b8 e) + (- (3 * r) * b2 e + -(b2 e + 12 * r) * (3 * r)) * (4 * b8 e))]
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * b8 e + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (3 * r * b6 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (3 * r * r * b4 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (r * r * r * b2 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (3 * r * r * r * r) - 8 * (b4 e + (r * b2 e + r * (6 * r))) ^ 3 - ((27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * b6 e + (27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * (2 * r * b4 e) + (27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * (r * r * b2 e) + (27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * (4 * r * r * r)) + (((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * b6 e + ((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * (2 * r * b4 e) + ((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * (r * r * b2 e) + ((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * (4 * r * r * r)) = -b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e + 9 * b2 e * b4 e * b6 e
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ -(b2 e ^ 2 * b8 e) + (-(3 * r) * b2 e + -(b2 e + 12 * r) * (3 * r)) * (4 * b8 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (3 * r * b6 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (3 * r * r * b4 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (r * r * r * b2 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (3 * r * r * r * r) - 8 * (b4 e + (r * b2 e + r * (6 * r))) ^ 3 - ((27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * b6 e + (27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * (2 * r * b4 e) + (27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * (r * r * b2 e) + (27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * (4 * r * r * r)) + (((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * b6 e + ((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * (2 * r * b4 e) + ((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * (r * r * b2 e) + ((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * (4 * r * r * r)) = -b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e + 9 * b2 e * b4 e * b6 e
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.rst_discr
[161, 1]
[167, 7]
rw [b8_identity]
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ -(b2 e ^ 2 * b8 e) + (-(3 * r) * b2 e + -(b2 e + 12 * r) * (3 * r)) * (4 * b8 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (3 * r * b6 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (3 * r * r * b4 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (r * r * r * b2 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (3 * r * r * r * r) - 8 * (b4 e + (r * b2 e + r * (6 * r))) ^ 3 - ((27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * b6 e + (27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * (2 * r * b4 e) + (27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * (r * r * b2 e) + (27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * (4 * r * r * r)) + (((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * b6 e + ((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * (2 * r * b4 e) + ((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * (r * r * b2 e) + ((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * (4 * r * r * r)) = -b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e + 9 * b2 e * b4 e * b6 e
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ -(b2 e ^ 2 * b8 e) + (-(3 * r) * b2 e + -(b2 e + 12 * r) * (3 * r)) * (b2 e * b6 e - b4 e ^ 2) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (3 * r * b6 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (3 * r * r * b4 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (r * r * r * b2 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (3 * r * r * r * r) - 8 * (b4 e + (r * b2 e + r * (6 * r))) ^ 3 - ((27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * b6 e + (27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * (2 * r * b4 e) + (27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * (r * r * b2 e) + (27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * (4 * r * r * r)) + (((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * b6 e + ((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * (2 * r * b4 e) + ((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * (r * r * b2 e) + ((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * (4 * r * r * r)) = -b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e + 9 * b2 e * b4 e * b6 e
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.rst_discr
[161, 1]
[167, 7]
ring
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ -(b2 e ^ 2 * b8 e) + (-(3 * r) * b2 e + -(b2 e + 12 * r) * (3 * r)) * (b2 e * b6 e - b4 e ^ 2) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (3 * r * b6 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (3 * r * r * b4 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (r * r * r * b2 e) + (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * (3 * r * r * r * r) - 8 * (b4 e + (r * b2 e + r * (6 * r))) ^ 3 - ((27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * b6 e + (27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * (2 * r * b4 e) + (27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * (r * r * b2 e) + (27 * b6 e + 27 * (2 * r * b4 e) + 27 * (r * r * b2 e) + 27 * (4 * r * r * r)) * (4 * r * r * r)) + (((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * b6 e + ((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * (2 * r * b4 e) + ((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * (r * r * b2 e) + ((9 * b2 e + 9 * (12 * r)) * b4 e + ((9 * b2 e + 9 * (12 * r)) * (r * b2 e) + (9 * b2 e + 9 * (12 * r)) * (r * (6 * r)))) * (4 * r * r * r)) = -b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e + 9 * b2 e * b4 e * b6 e
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.rst_discr
[161, 1]
[167, 7]
ring
R : Type u inst✝ : CommRing R r s t : R e : Model R ⊢ (-(b2 e + 12 * r) * b2 e + -(b2 e + 12 * r) * (12 * r)) * b8 e = -(b2 e ^ 2 * b8 e) + (-(3 * r) * b2 e + -(b2 e + 12 * r) * (3 * r)) * (4 * b8 e)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.map_b2
[176, 1]
[176, 67]
simp [Model.b2]
R✝ : Type u inst✝² : CommRing R✝ R S : Type u inst✝¹ : CommRing R inst✝ : CommRing S f : R →+* S e : Model R ⊢ b2 (map f e) = ↑f (b2 e)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.map_b4
[177, 1]
[177, 67]
simp [Model.b4]
R✝ : Type u inst✝² : CommRing R✝ R S : Type u inst✝¹ : CommRing R inst✝ : CommRing S f : R →+* S e : Model R ⊢ b4 (map f e) = ↑f (b4 e)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.map_b5
[178, 1]
[178, 67]
simp [Model.b5]
R✝ : Type u inst✝² : CommRing R✝ R S : Type u inst✝¹ : CommRing R inst✝ : CommRing S f : R →+* S e : Model R ⊢ b5 (map f e) = ↑f (b5 e)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.map_b6
[179, 1]
[179, 67]
simp [Model.b6]
R✝ : Type u inst✝² : CommRing R✝ R S : Type u inst✝¹ : CommRing R inst✝ : CommRing S f : R →+* S e : Model R ⊢ b6 (map f e) = ↑f (b6 e)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.map_b7
[180, 1]
[180, 67]
simp [Model.b7]
R✝ : Type u inst✝² : CommRing R✝ R S : Type u inst✝¹ : CommRing R inst✝ : CommRing S f : R →+* S e : Model R ⊢ b7 (map f e) = ↑f (b7 e)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.map_b8
[181, 1]
[181, 67]
simp [Model.b8]
R✝ : Type u inst✝² : CommRing R✝ R S : Type u inst✝¹ : CommRing R inst✝ : CommRing S f : R →+* S e : Model R ⊢ b8 (map f e) = ↑f (b8 e)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.map_c4
[183, 1]
[183, 67]
simp [Model.c4]
R✝ : Type u inst✝² : CommRing R✝ R S : Type u inst✝¹ : CommRing R inst✝ : CommRing S f : R →+* S e : Model R ⊢ c4 (map f e) = ↑f (c4 e)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.map_c6
[184, 1]
[184, 67]
simp [Model.c6]
R✝ : Type u inst✝² : CommRing R✝ R S : Type u inst✝¹ : CommRing R inst✝ : CommRing S f : R →+* S e : Model R ⊢ c6 (map f e) = ↑f (c6 e)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.map_discr
[186, 1]
[186, 79]
simp [Model.discr]
R✝ : Type u inst✝² : CommRing R✝ R S : Type u inst✝¹ : CommRing R inst✝ : CommRing S f : R →+* S e : Model R ⊢ discr (map f e) = ↑f (discr e)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.weierstrass_map
[203, 1]
[206, 22]
simp [weierstrass]
R✝ : Type u inst✝² : CommRing R✝ R S : Type u inst✝¹ : CommRing R inst✝ : CommRing S f : R →+* S e : Model R P : R × R ⊢ weierstrass (map f e) (Prod.map (↑f) (↑f) P) = ↑f (weierstrass e P)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.dweierstrass_dx_map
[208, 1]
[211, 26]
simp [dweierstrass_dx]
R✝ : Type u inst✝² : CommRing R✝ R S : Type u inst✝¹ : CommRing R inst✝ : CommRing S f : R →+* S e : Model R P : R × R ⊢ dweierstrass_dx (map f e) (Prod.map (↑f) (↑f) P) = ↑f (dweierstrass_dx e P)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.dweierstrass_dy_map
[213, 1]
[216, 26]
simp [dweierstrass_dy]
R✝ : Type u inst✝² : CommRing R✝ R S : Type u inst✝¹ : CommRing R inst✝ : CommRing S f : R →+* S e : Model R P : R × R ⊢ dweierstrass_dy (map f e) (Prod.map (↑f) (↑f) P) = ↑f (dweierstrass_dy e P)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.discr_eq_neg_singular
[220, 1]
[249, 7]
simp only [discr, weierstrass, dweierstrass_dx, dweierstrass_dy, b2, b4, b6, b8]
R : Type u inst✝ : CommRing R e : Model R ⊢ discr e = -(e.a1 ^ 4 * e.a2 * e.a3 ^ 2 - e.a1 ^ 5 * e.a3 * e.a4 + e.a1 ^ 6 * e.a6 + 8 * e.a1 ^ 2 * e.a2 ^ 2 * e.a3 ^ 2 - e.a1 ^ 3 * e.a3 ^ 3 - 8 * e.a1 ^ 3 * e.a2 * e.a3 * e.a4 - e.a1 ^ 4 * e.a4 ^ 2 + 12 * e.a1 ^ 4 * e.a2 * e.a6 + 16 * e.a2 ^ 3 * e.a3 ^ 2 - 36 * e.a1 * e.a2 * e.a3 ^ 3 - 16 * e.a1 * e.a2 ^ 2 * e.a3 * e.a4 + 30 * e.a1 ^ 2 * e.a3 ^ 2 * e.a4 - 8 * e.a1 ^ 2 * e.a2 * e.a4 ^ 2 + 48 * e.a1 ^ 2 * e.a2 ^ 2 * e.a6 - 36 * e.a1 ^ 3 * e.a3 * e.a6 + 27 * e.a3 ^ 4 - 72 * e.a2 * e.a3 ^ 2 * e.a4 - 16 * e.a2 ^ 2 * e.a4 ^ 2 + 96 * e.a1 * e.a3 * e.a4 ^ 2 + 64 * e.a2 ^ 3 * e.a6 - 144 * e.a1 * e.a2 * e.a3 * e.a6 - 72 * e.a1 ^ 2 * e.a4 * e.a6 + 64 * e.a4 ^ 3 + 216 * e.a3 ^ 2 * e.a6 - 288 * e.a2 * e.a4 * e.a6 + 432 * e.a6 ^ 2)
R : Type u inst✝ : CommRing R e : Model R ⊢ -(e.a1 * e.a1 + 4 * e.a2) * (e.a1 * e.a1 + 4 * e.a2) * (e.a1 * e.a1 * e.a6 - e.a1 * e.a3 * e.a4 + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 - e.a4 * e.a4) - 8 * (e.a1 * e.a3 + 2 * e.a4) ^ 3 - 27 * (e.a3 * e.a3 + 4 * e.a6) * (e.a3 * e.a3 + 4 * e.a6) + 9 * (e.a1 * e.a1 + 4 * e.a2) * (e.a1 * e.a3 + 2 * e.a4) * (e.a3 * e.a3 + 4 * e.a6) = -(e.a1 ^ 4 * e.a2 * e.a3 ^ 2 - e.a1 ^ 5 * e.a3 * e.a4 + e.a1 ^ 6 * e.a6 + 8 * e.a1 ^ 2 * e.a2 ^ 2 * e.a3 ^ 2 - e.a1 ^ 3 * e.a3 ^ 3 - 8 * e.a1 ^ 3 * e.a2 * e.a3 * e.a4 - e.a1 ^ 4 * e.a4 ^ 2 + 12 * e.a1 ^ 4 * e.a2 * e.a6 + 16 * e.a2 ^ 3 * e.a3 ^ 2 - 36 * e.a1 * e.a2 * e.a3 ^ 3 - 16 * e.a1 * e.a2 ^ 2 * e.a3 * e.a4 + 30 * e.a1 ^ 2 * e.a3 ^ 2 * e.a4 - 8 * e.a1 ^ 2 * e.a2 * e.a4 ^ 2 + 48 * e.a1 ^ 2 * e.a2 ^ 2 * e.a6 - 36 * e.a1 ^ 3 * e.a3 * e.a6 + 27 * e.a3 ^ 4 - 72 * e.a2 * e.a3 ^ 2 * e.a4 - 16 * e.a2 ^ 2 * e.a4 ^ 2 + 96 * e.a1 * e.a3 * e.a4 ^ 2 + 64 * e.a2 ^ 3 * e.a6 - 144 * e.a1 * e.a2 * e.a3 * e.a6 - 72 * e.a1 ^ 2 * e.a4 * e.a6 + 64 * e.a4 ^ 3 + 216 * e.a3 ^ 2 * e.a6 - 288 * e.a2 * e.a4 * e.a6 + 432 * e.a6 ^ 2)
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.discr_eq_neg_singular
[220, 1]
[249, 7]
ring
R : Type u inst✝ : CommRing R e : Model R ⊢ -(e.a1 * e.a1 + 4 * e.a2) * (e.a1 * e.a1 + 4 * e.a2) * (e.a1 * e.a1 * e.a6 - e.a1 * e.a3 * e.a4 + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 - e.a4 * e.a4) - 8 * (e.a1 * e.a3 + 2 * e.a4) ^ 3 - 27 * (e.a3 * e.a3 + 4 * e.a6) * (e.a3 * e.a3 + 4 * e.a6) + 9 * (e.a1 * e.a1 + 4 * e.a2) * (e.a1 * e.a3 + 2 * e.a4) * (e.a3 * e.a3 + 4 * e.a6) = -(e.a1 ^ 4 * e.a2 * e.a3 ^ 2 - e.a1 ^ 5 * e.a3 * e.a4 + e.a1 ^ 6 * e.a6 + 8 * e.a1 ^ 2 * e.a2 ^ 2 * e.a3 ^ 2 - e.a1 ^ 3 * e.a3 ^ 3 - 8 * e.a1 ^ 3 * e.a2 * e.a3 * e.a4 - e.a1 ^ 4 * e.a4 ^ 2 + 12 * e.a1 ^ 4 * e.a2 * e.a6 + 16 * e.a2 ^ 3 * e.a3 ^ 2 - 36 * e.a1 * e.a2 * e.a3 ^ 3 - 16 * e.a1 * e.a2 ^ 2 * e.a3 * e.a4 + 30 * e.a1 ^ 2 * e.a3 ^ 2 * e.a4 - 8 * e.a1 ^ 2 * e.a2 * e.a4 ^ 2 + 48 * e.a1 ^ 2 * e.a2 ^ 2 * e.a6 - 36 * e.a1 ^ 3 * e.a3 * e.a6 + 27 * e.a3 ^ 4 - 72 * e.a2 * e.a3 ^ 2 * e.a4 - 16 * e.a2 ^ 2 * e.a4 ^ 2 + 96 * e.a1 * e.a3 * e.a4 ^ 2 + 64 * e.a2 ^ 3 * e.a6 - 144 * e.a1 * e.a2 * e.a3 * e.a6 - 72 * e.a1 ^ 2 * e.a4 * e.a6 + 64 * e.a4 ^ 3 + 216 * e.a3 ^ 2 * e.a6 - 288 * e.a2 * e.a4 * e.a6 + 432 * e.a6 ^ 2)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.discr_in_jacobian_ideal
[253, 1]
[272, 7]
rw [discr_eq_neg_singular]
R : Type u inst✝ : CommRing R e : Model R P : R × R ⊢ discr e = -((48 * P.fst * P.snd * e.a2 ^ 2 + 24 * e.a1 * e.a2 * e.a6 + 216 * P.snd * e.a6 + P.snd * e.a1 ^ 6 + 11 * P.snd * e.a1 ^ 4 * e.a2 + P.fst * e.a1 ^ 4 * e.a3 + 38 * P.fst * e.a1 ^ 2 * e.a2 * e.a3 + 8 * e.a1 ^ 2 * e.a2 ^ 2 * e.a3 + e.a1 ^ 4 * e.a2 * e.a3 + 40 * P.snd * e.a1 ^ 2 * e.a2 ^ 2 + 32 * P.snd * e.a2 ^ 3 + 24 * P.fst * P.snd * e.a1 * e.a3 + 30 * P.fst ^ 2 * e.a2 * e.a3 + 3 * P.fst * e.a1 ^ 3 * e.a4 + 60 * P.fst ^ 2 * e.a1 * e.a4 + 30 * P.fst ^ 2 * e.a1 ^ 2 * e.a3 + 31 * e.a1 ^ 2 * e.a3 * e.a4 + 144 * P.snd ^ 2 * e.a3 + 198 * P.snd * e.a3 ^ 2 + 27 * e.a3 ^ 3 + 60 * e.a1 * e.a4 ^ 2 + 36 * P.fst * e.a1 * e.a6 + 76 * P.fst * e.a2 ^ 2 * e.a3 + 16 * e.a2 ^ 3 * e.a3 + 84 * P.fst * e.a1 * e.a2 * e.a4 - (36 * e.a3 * e.a6 + P.fst ^ 2 * e.a1 ^ 5 + P.fst * e.a1 ^ 5 * e.a2 + P.fst * P.snd * e.a1 ^ 4 + 9 * P.fst ^ 2 * e.a1 ^ 3 * e.a2 + 10 * P.fst * e.a1 ^ 3 * e.a2 ^ 2 + e.a1 ^ 5 * e.a4 + 6 * P.snd ^ 2 * e.a1 ^ 3 + 8 * P.fst * P.snd * e.a1 ^ 2 * e.a2 + 24 * P.fst ^ 2 * e.a1 * e.a2 ^ 2 + 32 * P.fst * e.a1 * e.a2 ^ 3 + 35 * P.snd * e.a1 ^ 3 * e.a3 + e.a1 ^ 3 * e.a3 ^ 2 + 9 * e.a1 ^ 3 * e.a2 * e.a4 + 48 * P.snd ^ 2 * e.a1 * e.a2 + 134 * P.snd * e.a1 * e.a2 * e.a3 + 27 * P.fst * e.a1 * e.a3 ^ 2 + 36 * e.a1 * e.a2 * e.a3 ^ 2 + 58 * P.snd * e.a1 ^ 2 * e.a4 + 24 * e.a1 * e.a2 ^ 2 * e.a4 + 144 * P.fst * P.snd * e.a4 + 120 * P.snd * e.a2 * e.a4 + 168 * P.fst * e.a3 * e.a4 + 34 * e.a2 * e.a3 * e.a4)) * dweierstrass_dy e P + (e.a1 ^ 2 * e.a3 ^ 2 + 12 * e.a1 ^ 2 * e.a6 + 16 * e.a2 ^ 2 * e.a4 + 32 * P.fst * e.a2 ^ 3 + e.a1 ^ 4 * e.a4 + 144 * P.fst * e.a6 + 48 * e.a2 * e.a6 + P.fst * e.a1 ^ 4 * e.a2 + 84 * P.fst * e.a3 ^ 2 + 56 * P.snd * e.a1 * e.a4 + 8 * e.a1 ^ 2 * e.a2 * e.a4 + 28 * P.snd * e.a1 ^ 2 * e.a3 + 52 * P.snd * e.a2 * e.a3 + 96 * P.fst * P.snd * e.a3 + 8 * P.fst * e.a1 ^ 2 * e.a2 ^ 2 + 38 * e.a2 * e.a3 ^ 2 + 32 * P.fst ^ 2 * e.a2 ^ 2 - (2 * P.fst * e.a1 ^ 3 * e.a3 + 112 * P.fst * e.a2 * e.a4 + e.a1 ^ 3 * e.a2 * e.a3 + 36 * e.a1 * e.a3 * e.a4 + 96 * P.fst ^ 2 * e.a4 + 32 * P.fst * P.snd * e.a1 * e.a2 + 32 * P.snd * e.a1 * e.a2 ^ 2 + 64 * e.a4 ^ 2 + 4 * P.fst * P.snd * e.a1 ^ 3 + 10 * P.snd * e.a1 ^ 3 * e.a2 + P.snd * e.a1 ^ 5 + 8 * e.a1 * e.a2 ^ 2 * e.a3 + 46 * P.fst * e.a1 * e.a2 * e.a3)) * dweierstrass_dx e P + (60 * e.a1 ^ 2 * e.a4 + 288 * P.fst * e.a4 + 240 * e.a2 * e.a4 + 12 * P.snd * e.a1 ^ 3 + 36 * e.a1 ^ 3 * e.a3 + 96 * P.snd * e.a1 * e.a2 + 168 * e.a1 * e.a2 * e.a3 - (432 * e.a6 + e.a1 ^ 6 + 288 * P.snd * e.a3 + 252 * e.a3 ^ 2 + 12 * e.a1 ^ 4 * e.a2 + 48 * e.a1 ^ 2 * e.a2 ^ 2 + 96 * P.fst * e.a2 ^ 2 + 64 * e.a2 ^ 3)) * weierstrass e P)
R : Type u inst✝ : CommRing R e : Model R P : R × R ⊢ -(e.a1 ^ 4 * e.a2 * e.a3 ^ 2 - e.a1 ^ 5 * e.a3 * e.a4 + e.a1 ^ 6 * e.a6 + 8 * e.a1 ^ 2 * e.a2 ^ 2 * e.a3 ^ 2 - e.a1 ^ 3 * e.a3 ^ 3 - 8 * e.a1 ^ 3 * e.a2 * e.a3 * e.a4 - e.a1 ^ 4 * e.a4 ^ 2 + 12 * e.a1 ^ 4 * e.a2 * e.a6 + 16 * e.a2 ^ 3 * e.a3 ^ 2 - 36 * e.a1 * e.a2 * e.a3 ^ 3 - 16 * e.a1 * e.a2 ^ 2 * e.a3 * e.a4 + 30 * e.a1 ^ 2 * e.a3 ^ 2 * e.a4 - 8 * e.a1 ^ 2 * e.a2 * e.a4 ^ 2 + 48 * e.a1 ^ 2 * e.a2 ^ 2 * e.a6 - 36 * e.a1 ^ 3 * e.a3 * e.a6 + 27 * e.a3 ^ 4 - 72 * e.a2 * e.a3 ^ 2 * e.a4 - 16 * e.a2 ^ 2 * e.a4 ^ 2 + 96 * e.a1 * e.a3 * e.a4 ^ 2 + 64 * e.a2 ^ 3 * e.a6 - 144 * e.a1 * e.a2 * e.a3 * e.a6 - 72 * e.a1 ^ 2 * e.a4 * e.a6 + 64 * e.a4 ^ 3 + 216 * e.a3 ^ 2 * e.a6 - 288 * e.a2 * e.a4 * e.a6 + 432 * e.a6 ^ 2) = -((48 * P.fst * P.snd * e.a2 ^ 2 + 24 * e.a1 * e.a2 * e.a6 + 216 * P.snd * e.a6 + P.snd * e.a1 ^ 6 + 11 * P.snd * e.a1 ^ 4 * e.a2 + P.fst * e.a1 ^ 4 * e.a3 + 38 * P.fst * e.a1 ^ 2 * e.a2 * e.a3 + 8 * e.a1 ^ 2 * e.a2 ^ 2 * e.a3 + e.a1 ^ 4 * e.a2 * e.a3 + 40 * P.snd * e.a1 ^ 2 * e.a2 ^ 2 + 32 * P.snd * e.a2 ^ 3 + 24 * P.fst * P.snd * e.a1 * e.a3 + 30 * P.fst ^ 2 * e.a2 * e.a3 + 3 * P.fst * e.a1 ^ 3 * e.a4 + 60 * P.fst ^ 2 * e.a1 * e.a4 + 30 * P.fst ^ 2 * e.a1 ^ 2 * e.a3 + 31 * e.a1 ^ 2 * e.a3 * e.a4 + 144 * P.snd ^ 2 * e.a3 + 198 * P.snd * e.a3 ^ 2 + 27 * e.a3 ^ 3 + 60 * e.a1 * e.a4 ^ 2 + 36 * P.fst * e.a1 * e.a6 + 76 * P.fst * e.a2 ^ 2 * e.a3 + 16 * e.a2 ^ 3 * e.a3 + 84 * P.fst * e.a1 * e.a2 * e.a4 - (36 * e.a3 * e.a6 + P.fst ^ 2 * e.a1 ^ 5 + P.fst * e.a1 ^ 5 * e.a2 + P.fst * P.snd * e.a1 ^ 4 + 9 * P.fst ^ 2 * e.a1 ^ 3 * e.a2 + 10 * P.fst * e.a1 ^ 3 * e.a2 ^ 2 + e.a1 ^ 5 * e.a4 + 6 * P.snd ^ 2 * e.a1 ^ 3 + 8 * P.fst * P.snd * e.a1 ^ 2 * e.a2 + 24 * P.fst ^ 2 * e.a1 * e.a2 ^ 2 + 32 * P.fst * e.a1 * e.a2 ^ 3 + 35 * P.snd * e.a1 ^ 3 * e.a3 + e.a1 ^ 3 * e.a3 ^ 2 + 9 * e.a1 ^ 3 * e.a2 * e.a4 + 48 * P.snd ^ 2 * e.a1 * e.a2 + 134 * P.snd * e.a1 * e.a2 * e.a3 + 27 * P.fst * e.a1 * e.a3 ^ 2 + 36 * e.a1 * e.a2 * e.a3 ^ 2 + 58 * P.snd * e.a1 ^ 2 * e.a4 + 24 * e.a1 * e.a2 ^ 2 * e.a4 + 144 * P.fst * P.snd * e.a4 + 120 * P.snd * e.a2 * e.a4 + 168 * P.fst * e.a3 * e.a4 + 34 * e.a2 * e.a3 * e.a4)) * dweierstrass_dy e P + (e.a1 ^ 2 * e.a3 ^ 2 + 12 * e.a1 ^ 2 * e.a6 + 16 * e.a2 ^ 2 * e.a4 + 32 * P.fst * e.a2 ^ 3 + e.a1 ^ 4 * e.a4 + 144 * P.fst * e.a6 + 48 * e.a2 * e.a6 + P.fst * e.a1 ^ 4 * e.a2 + 84 * P.fst * e.a3 ^ 2 + 56 * P.snd * e.a1 * e.a4 + 8 * e.a1 ^ 2 * e.a2 * e.a4 + 28 * P.snd * e.a1 ^ 2 * e.a3 + 52 * P.snd * e.a2 * e.a3 + 96 * P.fst * P.snd * e.a3 + 8 * P.fst * e.a1 ^ 2 * e.a2 ^ 2 + 38 * e.a2 * e.a3 ^ 2 + 32 * P.fst ^ 2 * e.a2 ^ 2 - (2 * P.fst * e.a1 ^ 3 * e.a3 + 112 * P.fst * e.a2 * e.a4 + e.a1 ^ 3 * e.a2 * e.a3 + 36 * e.a1 * e.a3 * e.a4 + 96 * P.fst ^ 2 * e.a4 + 32 * P.fst * P.snd * e.a1 * e.a2 + 32 * P.snd * e.a1 * e.a2 ^ 2 + 64 * e.a4 ^ 2 + 4 * P.fst * P.snd * e.a1 ^ 3 + 10 * P.snd * e.a1 ^ 3 * e.a2 + P.snd * e.a1 ^ 5 + 8 * e.a1 * e.a2 ^ 2 * e.a3 + 46 * P.fst * e.a1 * e.a2 * e.a3)) * dweierstrass_dx e P + (60 * e.a1 ^ 2 * e.a4 + 288 * P.fst * e.a4 + 240 * e.a2 * e.a4 + 12 * P.snd * e.a1 ^ 3 + 36 * e.a1 ^ 3 * e.a3 + 96 * P.snd * e.a1 * e.a2 + 168 * e.a1 * e.a2 * e.a3 - (432 * e.a6 + e.a1 ^ 6 + 288 * P.snd * e.a3 + 252 * e.a3 ^ 2 + 12 * e.a1 ^ 4 * e.a2 + 48 * e.a1 ^ 2 * e.a2 ^ 2 + 96 * P.fst * e.a2 ^ 2 + 64 * e.a2 ^ 3)) * weierstrass e P)
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.discr_in_jacobian_ideal
[253, 1]
[272, 7]
simp only [weierstrass, dweierstrass_dx, dweierstrass_dy]
R : Type u inst✝ : CommRing R e : Model R P : R × R ⊢ -(e.a1 ^ 4 * e.a2 * e.a3 ^ 2 - e.a1 ^ 5 * e.a3 * e.a4 + e.a1 ^ 6 * e.a6 + 8 * e.a1 ^ 2 * e.a2 ^ 2 * e.a3 ^ 2 - e.a1 ^ 3 * e.a3 ^ 3 - 8 * e.a1 ^ 3 * e.a2 * e.a3 * e.a4 - e.a1 ^ 4 * e.a4 ^ 2 + 12 * e.a1 ^ 4 * e.a2 * e.a6 + 16 * e.a2 ^ 3 * e.a3 ^ 2 - 36 * e.a1 * e.a2 * e.a3 ^ 3 - 16 * e.a1 * e.a2 ^ 2 * e.a3 * e.a4 + 30 * e.a1 ^ 2 * e.a3 ^ 2 * e.a4 - 8 * e.a1 ^ 2 * e.a2 * e.a4 ^ 2 + 48 * e.a1 ^ 2 * e.a2 ^ 2 * e.a6 - 36 * e.a1 ^ 3 * e.a3 * e.a6 + 27 * e.a3 ^ 4 - 72 * e.a2 * e.a3 ^ 2 * e.a4 - 16 * e.a2 ^ 2 * e.a4 ^ 2 + 96 * e.a1 * e.a3 * e.a4 ^ 2 + 64 * e.a2 ^ 3 * e.a6 - 144 * e.a1 * e.a2 * e.a3 * e.a6 - 72 * e.a1 ^ 2 * e.a4 * e.a6 + 64 * e.a4 ^ 3 + 216 * e.a3 ^ 2 * e.a6 - 288 * e.a2 * e.a4 * e.a6 + 432 * e.a6 ^ 2) = -((48 * P.fst * P.snd * e.a2 ^ 2 + 24 * e.a1 * e.a2 * e.a6 + 216 * P.snd * e.a6 + P.snd * e.a1 ^ 6 + 11 * P.snd * e.a1 ^ 4 * e.a2 + P.fst * e.a1 ^ 4 * e.a3 + 38 * P.fst * e.a1 ^ 2 * e.a2 * e.a3 + 8 * e.a1 ^ 2 * e.a2 ^ 2 * e.a3 + e.a1 ^ 4 * e.a2 * e.a3 + 40 * P.snd * e.a1 ^ 2 * e.a2 ^ 2 + 32 * P.snd * e.a2 ^ 3 + 24 * P.fst * P.snd * e.a1 * e.a3 + 30 * P.fst ^ 2 * e.a2 * e.a3 + 3 * P.fst * e.a1 ^ 3 * e.a4 + 60 * P.fst ^ 2 * e.a1 * e.a4 + 30 * P.fst ^ 2 * e.a1 ^ 2 * e.a3 + 31 * e.a1 ^ 2 * e.a3 * e.a4 + 144 * P.snd ^ 2 * e.a3 + 198 * P.snd * e.a3 ^ 2 + 27 * e.a3 ^ 3 + 60 * e.a1 * e.a4 ^ 2 + 36 * P.fst * e.a1 * e.a6 + 76 * P.fst * e.a2 ^ 2 * e.a3 + 16 * e.a2 ^ 3 * e.a3 + 84 * P.fst * e.a1 * e.a2 * e.a4 - (36 * e.a3 * e.a6 + P.fst ^ 2 * e.a1 ^ 5 + P.fst * e.a1 ^ 5 * e.a2 + P.fst * P.snd * e.a1 ^ 4 + 9 * P.fst ^ 2 * e.a1 ^ 3 * e.a2 + 10 * P.fst * e.a1 ^ 3 * e.a2 ^ 2 + e.a1 ^ 5 * e.a4 + 6 * P.snd ^ 2 * e.a1 ^ 3 + 8 * P.fst * P.snd * e.a1 ^ 2 * e.a2 + 24 * P.fst ^ 2 * e.a1 * e.a2 ^ 2 + 32 * P.fst * e.a1 * e.a2 ^ 3 + 35 * P.snd * e.a1 ^ 3 * e.a3 + e.a1 ^ 3 * e.a3 ^ 2 + 9 * e.a1 ^ 3 * e.a2 * e.a4 + 48 * P.snd ^ 2 * e.a1 * e.a2 + 134 * P.snd * e.a1 * e.a2 * e.a3 + 27 * P.fst * e.a1 * e.a3 ^ 2 + 36 * e.a1 * e.a2 * e.a3 ^ 2 + 58 * P.snd * e.a1 ^ 2 * e.a4 + 24 * e.a1 * e.a2 ^ 2 * e.a4 + 144 * P.fst * P.snd * e.a4 + 120 * P.snd * e.a2 * e.a4 + 168 * P.fst * e.a3 * e.a4 + 34 * e.a2 * e.a3 * e.a4)) * dweierstrass_dy e P + (e.a1 ^ 2 * e.a3 ^ 2 + 12 * e.a1 ^ 2 * e.a6 + 16 * e.a2 ^ 2 * e.a4 + 32 * P.fst * e.a2 ^ 3 + e.a1 ^ 4 * e.a4 + 144 * P.fst * e.a6 + 48 * e.a2 * e.a6 + P.fst * e.a1 ^ 4 * e.a2 + 84 * P.fst * e.a3 ^ 2 + 56 * P.snd * e.a1 * e.a4 + 8 * e.a1 ^ 2 * e.a2 * e.a4 + 28 * P.snd * e.a1 ^ 2 * e.a3 + 52 * P.snd * e.a2 * e.a3 + 96 * P.fst * P.snd * e.a3 + 8 * P.fst * e.a1 ^ 2 * e.a2 ^ 2 + 38 * e.a2 * e.a3 ^ 2 + 32 * P.fst ^ 2 * e.a2 ^ 2 - (2 * P.fst * e.a1 ^ 3 * e.a3 + 112 * P.fst * e.a2 * e.a4 + e.a1 ^ 3 * e.a2 * e.a3 + 36 * e.a1 * e.a3 * e.a4 + 96 * P.fst ^ 2 * e.a4 + 32 * P.fst * P.snd * e.a1 * e.a2 + 32 * P.snd * e.a1 * e.a2 ^ 2 + 64 * e.a4 ^ 2 + 4 * P.fst * P.snd * e.a1 ^ 3 + 10 * P.snd * e.a1 ^ 3 * e.a2 + P.snd * e.a1 ^ 5 + 8 * e.a1 * e.a2 ^ 2 * e.a3 + 46 * P.fst * e.a1 * e.a2 * e.a3)) * dweierstrass_dx e P + (60 * e.a1 ^ 2 * e.a4 + 288 * P.fst * e.a4 + 240 * e.a2 * e.a4 + 12 * P.snd * e.a1 ^ 3 + 36 * e.a1 ^ 3 * e.a3 + 96 * P.snd * e.a1 * e.a2 + 168 * e.a1 * e.a2 * e.a3 - (432 * e.a6 + e.a1 ^ 6 + 288 * P.snd * e.a3 + 252 * e.a3 ^ 2 + 12 * e.a1 ^ 4 * e.a2 + 48 * e.a1 ^ 2 * e.a2 ^ 2 + 96 * P.fst * e.a2 ^ 2 + 64 * e.a2 ^ 3)) * weierstrass e P)
R : Type u inst✝ : CommRing R e : Model R P : R × R ⊢ -(e.a1 ^ 4 * e.a2 * e.a3 ^ 2 - e.a1 ^ 5 * e.a3 * e.a4 + e.a1 ^ 6 * e.a6 + 8 * e.a1 ^ 2 * e.a2 ^ 2 * e.a3 ^ 2 - e.a1 ^ 3 * e.a3 ^ 3 - 8 * e.a1 ^ 3 * e.a2 * e.a3 * e.a4 - e.a1 ^ 4 * e.a4 ^ 2 + 12 * e.a1 ^ 4 * e.a2 * e.a6 + 16 * e.a2 ^ 3 * e.a3 ^ 2 - 36 * e.a1 * e.a2 * e.a3 ^ 3 - 16 * e.a1 * e.a2 ^ 2 * e.a3 * e.a4 + 30 * e.a1 ^ 2 * e.a3 ^ 2 * e.a4 - 8 * e.a1 ^ 2 * e.a2 * e.a4 ^ 2 + 48 * e.a1 ^ 2 * e.a2 ^ 2 * e.a6 - 36 * e.a1 ^ 3 * e.a3 * e.a6 + 27 * e.a3 ^ 4 - 72 * e.a2 * e.a3 ^ 2 * e.a4 - 16 * e.a2 ^ 2 * e.a4 ^ 2 + 96 * e.a1 * e.a3 * e.a4 ^ 2 + 64 * e.a2 ^ 3 * e.a6 - 144 * e.a1 * e.a2 * e.a3 * e.a6 - 72 * e.a1 ^ 2 * e.a4 * e.a6 + 64 * e.a4 ^ 3 + 216 * e.a3 ^ 2 * e.a6 - 288 * e.a2 * e.a4 * e.a6 + 432 * e.a6 ^ 2) = -((48 * P.fst * P.snd * e.a2 ^ 2 + 24 * e.a1 * e.a2 * e.a6 + 216 * P.snd * e.a6 + P.snd * e.a1 ^ 6 + 11 * P.snd * e.a1 ^ 4 * e.a2 + P.fst * e.a1 ^ 4 * e.a3 + 38 * P.fst * e.a1 ^ 2 * e.a2 * e.a3 + 8 * e.a1 ^ 2 * e.a2 ^ 2 * e.a3 + e.a1 ^ 4 * e.a2 * e.a3 + 40 * P.snd * e.a1 ^ 2 * e.a2 ^ 2 + 32 * P.snd * e.a2 ^ 3 + 24 * P.fst * P.snd * e.a1 * e.a3 + 30 * P.fst ^ 2 * e.a2 * e.a3 + 3 * P.fst * e.a1 ^ 3 * e.a4 + 60 * P.fst ^ 2 * e.a1 * e.a4 + 30 * P.fst ^ 2 * e.a1 ^ 2 * e.a3 + 31 * e.a1 ^ 2 * e.a3 * e.a4 + 144 * P.snd ^ 2 * e.a3 + 198 * P.snd * e.a3 ^ 2 + 27 * e.a3 ^ 3 + 60 * e.a1 * e.a4 ^ 2 + 36 * P.fst * e.a1 * e.a6 + 76 * P.fst * e.a2 ^ 2 * e.a3 + 16 * e.a2 ^ 3 * e.a3 + 84 * P.fst * e.a1 * e.a2 * e.a4 - (36 * e.a3 * e.a6 + P.fst ^ 2 * e.a1 ^ 5 + P.fst * e.a1 ^ 5 * e.a2 + P.fst * P.snd * e.a1 ^ 4 + 9 * P.fst ^ 2 * e.a1 ^ 3 * e.a2 + 10 * P.fst * e.a1 ^ 3 * e.a2 ^ 2 + e.a1 ^ 5 * e.a4 + 6 * P.snd ^ 2 * e.a1 ^ 3 + 8 * P.fst * P.snd * e.a1 ^ 2 * e.a2 + 24 * P.fst ^ 2 * e.a1 * e.a2 ^ 2 + 32 * P.fst * e.a1 * e.a2 ^ 3 + 35 * P.snd * e.a1 ^ 3 * e.a3 + e.a1 ^ 3 * e.a3 ^ 2 + 9 * e.a1 ^ 3 * e.a2 * e.a4 + 48 * P.snd ^ 2 * e.a1 * e.a2 + 134 * P.snd * e.a1 * e.a2 * e.a3 + 27 * P.fst * e.a1 * e.a3 ^ 2 + 36 * e.a1 * e.a2 * e.a3 ^ 2 + 58 * P.snd * e.a1 ^ 2 * e.a4 + 24 * e.a1 * e.a2 ^ 2 * e.a4 + 144 * P.fst * P.snd * e.a4 + 120 * P.snd * e.a2 * e.a4 + 168 * P.fst * e.a3 * e.a4 + 34 * e.a2 * e.a3 * e.a4)) * (2 * P.snd + e.a1 * P.fst + e.a3) + (e.a1 ^ 2 * e.a3 ^ 2 + 12 * e.a1 ^ 2 * e.a6 + 16 * e.a2 ^ 2 * e.a4 + 32 * P.fst * e.a2 ^ 3 + e.a1 ^ 4 * e.a4 + 144 * P.fst * e.a6 + 48 * e.a2 * e.a6 + P.fst * e.a1 ^ 4 * e.a2 + 84 * P.fst * e.a3 ^ 2 + 56 * P.snd * e.a1 * e.a4 + 8 * e.a1 ^ 2 * e.a2 * e.a4 + 28 * P.snd * e.a1 ^ 2 * e.a3 + 52 * P.snd * e.a2 * e.a3 + 96 * P.fst * P.snd * e.a3 + 8 * P.fst * e.a1 ^ 2 * e.a2 ^ 2 + 38 * e.a2 * e.a3 ^ 2 + 32 * P.fst ^ 2 * e.a2 ^ 2 - (2 * P.fst * e.a1 ^ 3 * e.a3 + 112 * P.fst * e.a2 * e.a4 + e.a1 ^ 3 * e.a2 * e.a3 + 36 * e.a1 * e.a3 * e.a4 + 96 * P.fst ^ 2 * e.a4 + 32 * P.fst * P.snd * e.a1 * e.a2 + 32 * P.snd * e.a1 * e.a2 ^ 2 + 64 * e.a4 ^ 2 + 4 * P.fst * P.snd * e.a1 ^ 3 + 10 * P.snd * e.a1 ^ 3 * e.a2 + P.snd * e.a1 ^ 5 + 8 * e.a1 * e.a2 ^ 2 * e.a3 + 46 * P.fst * e.a1 * e.a2 * e.a3)) * (e.a1 * P.snd - (3 * P.fst ^ 2 + 2 * e.a2 * P.fst + e.a4)) + (60 * e.a1 ^ 2 * e.a4 + 288 * P.fst * e.a4 + 240 * e.a2 * e.a4 + 12 * P.snd * e.a1 ^ 3 + 36 * e.a1 ^ 3 * e.a3 + 96 * P.snd * e.a1 * e.a2 + 168 * e.a1 * e.a2 * e.a3 - (432 * e.a6 + e.a1 ^ 6 + 288 * P.snd * e.a3 + 252 * e.a3 ^ 2 + 12 * e.a1 ^ 4 * e.a2 + 48 * e.a1 ^ 2 * e.a2 ^ 2 + 96 * P.fst * e.a2 ^ 2 + 64 * e.a2 ^ 3)) * (P.snd ^ 2 + e.a1 * P.fst * P.snd + e.a3 * P.snd - (P.fst ^ 3 + e.a2 * P.fst ^ 2 + e.a4 * P.fst + e.a6)))
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.discr_in_jacobian_ideal
[253, 1]
[272, 7]
ring
R : Type u inst✝ : CommRing R e : Model R P : R × R ⊢ -(e.a1 ^ 4 * e.a2 * e.a3 ^ 2 - e.a1 ^ 5 * e.a3 * e.a4 + e.a1 ^ 6 * e.a6 + 8 * e.a1 ^ 2 * e.a2 ^ 2 * e.a3 ^ 2 - e.a1 ^ 3 * e.a3 ^ 3 - 8 * e.a1 ^ 3 * e.a2 * e.a3 * e.a4 - e.a1 ^ 4 * e.a4 ^ 2 + 12 * e.a1 ^ 4 * e.a2 * e.a6 + 16 * e.a2 ^ 3 * e.a3 ^ 2 - 36 * e.a1 * e.a2 * e.a3 ^ 3 - 16 * e.a1 * e.a2 ^ 2 * e.a3 * e.a4 + 30 * e.a1 ^ 2 * e.a3 ^ 2 * e.a4 - 8 * e.a1 ^ 2 * e.a2 * e.a4 ^ 2 + 48 * e.a1 ^ 2 * e.a2 ^ 2 * e.a6 - 36 * e.a1 ^ 3 * e.a3 * e.a6 + 27 * e.a3 ^ 4 - 72 * e.a2 * e.a3 ^ 2 * e.a4 - 16 * e.a2 ^ 2 * e.a4 ^ 2 + 96 * e.a1 * e.a3 * e.a4 ^ 2 + 64 * e.a2 ^ 3 * e.a6 - 144 * e.a1 * e.a2 * e.a3 * e.a6 - 72 * e.a1 ^ 2 * e.a4 * e.a6 + 64 * e.a4 ^ 3 + 216 * e.a3 ^ 2 * e.a6 - 288 * e.a2 * e.a4 * e.a6 + 432 * e.a6 ^ 2) = -((48 * P.fst * P.snd * e.a2 ^ 2 + 24 * e.a1 * e.a2 * e.a6 + 216 * P.snd * e.a6 + P.snd * e.a1 ^ 6 + 11 * P.snd * e.a1 ^ 4 * e.a2 + P.fst * e.a1 ^ 4 * e.a3 + 38 * P.fst * e.a1 ^ 2 * e.a2 * e.a3 + 8 * e.a1 ^ 2 * e.a2 ^ 2 * e.a3 + e.a1 ^ 4 * e.a2 * e.a3 + 40 * P.snd * e.a1 ^ 2 * e.a2 ^ 2 + 32 * P.snd * e.a2 ^ 3 + 24 * P.fst * P.snd * e.a1 * e.a3 + 30 * P.fst ^ 2 * e.a2 * e.a3 + 3 * P.fst * e.a1 ^ 3 * e.a4 + 60 * P.fst ^ 2 * e.a1 * e.a4 + 30 * P.fst ^ 2 * e.a1 ^ 2 * e.a3 + 31 * e.a1 ^ 2 * e.a3 * e.a4 + 144 * P.snd ^ 2 * e.a3 + 198 * P.snd * e.a3 ^ 2 + 27 * e.a3 ^ 3 + 60 * e.a1 * e.a4 ^ 2 + 36 * P.fst * e.a1 * e.a6 + 76 * P.fst * e.a2 ^ 2 * e.a3 + 16 * e.a2 ^ 3 * e.a3 + 84 * P.fst * e.a1 * e.a2 * e.a4 - (36 * e.a3 * e.a6 + P.fst ^ 2 * e.a1 ^ 5 + P.fst * e.a1 ^ 5 * e.a2 + P.fst * P.snd * e.a1 ^ 4 + 9 * P.fst ^ 2 * e.a1 ^ 3 * e.a2 + 10 * P.fst * e.a1 ^ 3 * e.a2 ^ 2 + e.a1 ^ 5 * e.a4 + 6 * P.snd ^ 2 * e.a1 ^ 3 + 8 * P.fst * P.snd * e.a1 ^ 2 * e.a2 + 24 * P.fst ^ 2 * e.a1 * e.a2 ^ 2 + 32 * P.fst * e.a1 * e.a2 ^ 3 + 35 * P.snd * e.a1 ^ 3 * e.a3 + e.a1 ^ 3 * e.a3 ^ 2 + 9 * e.a1 ^ 3 * e.a2 * e.a4 + 48 * P.snd ^ 2 * e.a1 * e.a2 + 134 * P.snd * e.a1 * e.a2 * e.a3 + 27 * P.fst * e.a1 * e.a3 ^ 2 + 36 * e.a1 * e.a2 * e.a3 ^ 2 + 58 * P.snd * e.a1 ^ 2 * e.a4 + 24 * e.a1 * e.a2 ^ 2 * e.a4 + 144 * P.fst * P.snd * e.a4 + 120 * P.snd * e.a2 * e.a4 + 168 * P.fst * e.a3 * e.a4 + 34 * e.a2 * e.a3 * e.a4)) * (2 * P.snd + e.a1 * P.fst + e.a3) + (e.a1 ^ 2 * e.a3 ^ 2 + 12 * e.a1 ^ 2 * e.a6 + 16 * e.a2 ^ 2 * e.a4 + 32 * P.fst * e.a2 ^ 3 + e.a1 ^ 4 * e.a4 + 144 * P.fst * e.a6 + 48 * e.a2 * e.a6 + P.fst * e.a1 ^ 4 * e.a2 + 84 * P.fst * e.a3 ^ 2 + 56 * P.snd * e.a1 * e.a4 + 8 * e.a1 ^ 2 * e.a2 * e.a4 + 28 * P.snd * e.a1 ^ 2 * e.a3 + 52 * P.snd * e.a2 * e.a3 + 96 * P.fst * P.snd * e.a3 + 8 * P.fst * e.a1 ^ 2 * e.a2 ^ 2 + 38 * e.a2 * e.a3 ^ 2 + 32 * P.fst ^ 2 * e.a2 ^ 2 - (2 * P.fst * e.a1 ^ 3 * e.a3 + 112 * P.fst * e.a2 * e.a4 + e.a1 ^ 3 * e.a2 * e.a3 + 36 * e.a1 * e.a3 * e.a4 + 96 * P.fst ^ 2 * e.a4 + 32 * P.fst * P.snd * e.a1 * e.a2 + 32 * P.snd * e.a1 * e.a2 ^ 2 + 64 * e.a4 ^ 2 + 4 * P.fst * P.snd * e.a1 ^ 3 + 10 * P.snd * e.a1 ^ 3 * e.a2 + P.snd * e.a1 ^ 5 + 8 * e.a1 * e.a2 ^ 2 * e.a3 + 46 * P.fst * e.a1 * e.a2 * e.a3)) * (e.a1 * P.snd - (3 * P.fst ^ 2 + 2 * e.a2 * P.fst + e.a4)) + (60 * e.a1 ^ 2 * e.a4 + 288 * P.fst * e.a4 + 240 * e.a2 * e.a4 + 12 * P.snd * e.a1 ^ 3 + 36 * e.a1 ^ 3 * e.a3 + 96 * P.snd * e.a1 * e.a2 + 168 * e.a1 * e.a2 * e.a3 - (432 * e.a6 + e.a1 ^ 6 + 288 * P.snd * e.a3 + 252 * e.a3 ^ 2 + 12 * e.a1 ^ 4 * e.a2 + 48 * e.a1 ^ 2 * e.a2 ^ 2 + 96 * P.fst * e.a2 ^ 2 + 64 * e.a2 ^ 3)) * (P.snd ^ 2 + e.a1 * P.fst * P.snd + e.a3 * P.snd - (P.fst ^ 3 + e.a2 * P.fst ^ 2 + e.a4 * P.fst + e.a6)))
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.var_change_comp
[277, 1]
[283, 7]
simp only [var_change, Prod.mk.injEq]
R : Type u inst✝ : CommRing R r s t r' s' t' : R P : R × R ⊢ var_change r s t (var_change r' s' t' P) = var_change (r + r') (s + s') (t + t' + s * r') P
R : Type u inst✝ : CommRing R r s t r' s' t' : R P : R × R ⊢ P.fst + r' + r = P.fst + (r + r') ∧ P.snd + s' * P.fst + t' + s * (P.fst + r') + t = P.snd + (s + s') * P.fst + (t + t' + s * r')
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.var_change_comp
[277, 1]
[283, 7]
apply And.intro <;> ring
R : Type u inst✝ : CommRing R r s t r' s' t' : R P : R × R ⊢ P.fst + r' + r = P.fst + (r + r') ∧ P.snd + s' * P.fst + t' + s * (P.fst + r') + t = P.snd + (s + s') * P.fst + (t + t' + s * r')
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.var_change_zero
[285, 1]
[287, 21]
simp [var_change]
R : Type u inst✝ : CommRing R P : R × R ⊢ var_change 0 0 0 P = P
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.weierstrass_iso_eq_var_change
[291, 1]
[295, 7]
simp only [weierstrass, rst_iso, var_change]
R : Type u inst✝ : CommRing R r s t : R e : Model R P : R × R ⊢ weierstrass (rst_iso r s t e) P = weierstrass e (var_change r s t P)
R : Type u inst✝ : CommRing R r s t : R e : Model R P : R × R ⊢ P.snd ^ 2 + (e.a1 + 2 * s) * P.fst * P.snd + (e.a3 + r * e.a1 + 2 * t) * P.snd - (P.fst ^ 3 + (e.a2 - s * e.a1 + 3 * r - s * s) * P.fst ^ 2 + (e.a4 - s * e.a3 + 2 * r * e.a2 - (t + r * s) * e.a1 + 3 * r * r - 2 * s * t) * P.fst + (e.a6 + r * e.a4 + r * r * e.a2 + r * r * r - t * (e.a3 + t + r * e.a1))) = (P.snd + s * P.fst + t) ^ 2 + e.a1 * (P.fst + r) * (P.snd + s * P.fst + t) + e.a3 * (P.snd + s * P.fst + t) - ((P.fst + r) ^ 3 + e.a2 * (P.fst + r) ^ 2 + e.a4 * (P.fst + r) + e.a6)
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.weierstrass_iso_eq_var_change
[291, 1]
[295, 7]
ring
R : Type u inst✝ : CommRing R r s t : R e : Model R P : R × R ⊢ P.snd ^ 2 + (e.a1 + 2 * s) * P.fst * P.snd + (e.a3 + r * e.a1 + 2 * t) * P.snd - (P.fst ^ 3 + (e.a2 - s * e.a1 + 3 * r - s * s) * P.fst ^ 2 + (e.a4 - s * e.a3 + 2 * r * e.a2 - (t + r * s) * e.a1 + 3 * r * r - 2 * s * t) * P.fst + (e.a6 + r * e.a4 + r * r * e.a2 + r * r * r - t * (e.a3 + t + r * e.a1))) = (P.snd + s * P.fst + t) ^ 2 + e.a1 * (P.fst + r) * (P.snd + s * P.fst + t) + e.a3 * (P.snd + s * P.fst + t) - ((P.fst + r) ^ 3 + e.a2 * (P.fst + r) ^ 2 + e.a4 * (P.fst + r) + e.a6)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.dweierstrass_dx_iso_eq_var_change
[297, 1]
[302, 7]
simp only [dweierstrass_dx, dweierstrass_dy, rst_iso, var_change]
R : Type u inst✝ : CommRing R r s t : R e : Model R P : R × R ⊢ dweierstrass_dx (rst_iso r s t e) P = dweierstrass_dx e (var_change r s t P) + s * dweierstrass_dy e (var_change r s t P)
R : Type u inst✝ : CommRing R r s t : R e : Model R P : R × R ⊢ (e.a1 + 2 * s) * P.snd - (3 * P.fst ^ 2 + 2 * (e.a2 - s * e.a1 + 3 * r - s * s) * P.fst + (e.a4 - s * e.a3 + 2 * r * e.a2 - (t + r * s) * e.a1 + 3 * r * r - 2 * s * t)) = e.a1 * (P.snd + s * P.fst + t) - (3 * (P.fst + r) ^ 2 + 2 * e.a2 * (P.fst + r) + e.a4) + s * (2 * (P.snd + s * P.fst + t) + e.a1 * (P.fst + r) + e.a3)
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.dweierstrass_dx_iso_eq_var_change
[297, 1]
[302, 7]
ring
R : Type u inst✝ : CommRing R r s t : R e : Model R P : R × R ⊢ (e.a1 + 2 * s) * P.snd - (3 * P.fst ^ 2 + 2 * (e.a2 - s * e.a1 + 3 * r - s * s) * P.fst + (e.a4 - s * e.a3 + 2 * r * e.a2 - (t + r * s) * e.a1 + 3 * r * r - 2 * s * t)) = e.a1 * (P.snd + s * P.fst + t) - (3 * (P.fst + r) ^ 2 + 2 * e.a2 * (P.fst + r) + e.a4) + s * (2 * (P.snd + s * P.fst + t) + e.a1 * (P.fst + r) + e.a3)
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.dweierstrass_dy_iso_eq_var_change
[304, 1]
[308, 7]
simp only [dweierstrass_dy, rst_iso, var_change]
R : Type u inst✝ : CommRing R r s t : R e : Model R P : R × R ⊢ dweierstrass_dy (rst_iso r s t e) P = dweierstrass_dy e (var_change r s t P)
R : Type u inst✝ : CommRing R r s t : R e : Model R P : R × R ⊢ 2 * P.snd + (e.a1 + 2 * s) * P.fst + (e.a3 + r * e.a1 + 2 * t) = 2 * (P.snd + s * P.fst + t) + e.a1 * (P.fst + r) + e.a3
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.dweierstrass_dy_iso_eq_var_change
[304, 1]
[308, 7]
ring
R : Type u inst✝ : CommRing R r s t : R e : Model R P : R × R ⊢ 2 * P.snd + (e.a1 + 2 * s) * P.fst + (e.a3 + r * e.a1 + 2 * t) = 2 * (P.snd + s * P.fst + t) + e.a1 * (P.fst + r) + e.a3
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
ValidModel.rt_of_a1
[336, 1]
[338, 67]
simp only [rst_iso, Model.rst_iso, mul_zero, add_zero, one_mul]
R : Type u inst✝ : CommRing R e : ValidModel R r t : R ⊢ (rst_iso r 0 t e).toModel.a1 = e.a1
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
ValidModel.t_of_a2
[340, 1]
[341, 96]
simp only [rst_iso, Model.rst_iso, one_pow, zero_mul, sub_zero, mul_zero, add_zero, one_mul]
R : Type u inst✝ : CommRing R e : ValidModel R t : R ⊢ (rst_iso 0 0 t e).toModel.a2 = e.a2
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
ValidModel.r_of_a2
[343, 1]
[344, 96]
simp only [rst_iso, Model.rst_iso, one_pow, zero_mul, sub_zero, mul_zero, add_zero, one_mul]
R : Type u inst✝ : CommRing R e : ValidModel R r : R ⊢ (rst_iso r 0 0 e).toModel.a2 = e.a2 + 3 * r
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
ValidModel.t_of_a3
[346, 1]
[347, 96]
simp only [rst_iso, Model.rst_iso, one_pow, zero_mul, sub_zero, mul_zero, add_zero, one_mul]
R : Type u inst✝ : CommRing R e : ValidModel R t : R ⊢ (rst_iso 0 0 t e).toModel.a3 = e.a3 + 2 * t
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
ValidModel.r_of_a3
[349, 1]
[350, 96]
simp only [rst_iso, Model.rst_iso, one_pow, zero_mul, sub_zero, mul_zero, add_zero, one_mul]
R : Type u inst✝ : CommRing R e : ValidModel R r : R ⊢ (rst_iso r 0 0 e).toModel.a3 = e.a3 + r * e.a1
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
ValidModel.t_of_a4
[352, 1]
[353, 96]
simp only [rst_iso, Model.rst_iso, one_pow, zero_mul, sub_zero, mul_zero, add_zero, one_mul]
R : Type u inst✝ : CommRing R e : ValidModel R t : R ⊢ (rst_iso 0 0 t e).toModel.a4 = e.a4 - t * e.a1
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
ValidModel.r_of_a4
[355, 1]
[357, 64]
simp only [rst_iso, Model.rst_iso, one_pow, zero_mul, sub_zero, mul_zero, one_mul, add_zero, mul_assoc, ←pow_two r]
R : Type u inst✝ : CommRing R e : ValidModel R r : R ⊢ (rst_iso r 0 0 e).toModel.a4 = e.a4 + 2 * r * e.a2 + 3 * r ^ 2
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
ValidModel.t_of_a6
[359, 1]
[361, 79]
simp only [rst_iso, Model.rst_iso, one_pow, zero_mul, sub_zero, mul_zero, one_mul, add_zero, mul_add, ←pow_two t, sub_eq_add_neg, neg_add, ←add_assoc]
R : Type u inst✝ : CommRing R e : ValidModel R t : R ⊢ (rst_iso 0 0 t e).toModel.a6 = e.a6 - t * e.a3 - t ^ 2
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
ValidModel.r_of_a6
[363, 1]
[366, 84]
simp only [rst_iso, Model.rst_iso, one_pow, zero_mul, sub_zero, mul_zero, one_mul, add_zero, mul_assoc, pow_two r, pow_succ r, pow_zero, mul_one]
R : Type u inst✝ : CommRing R e : ValidModel R r : R ⊢ (rst_iso r 0 0 e).toModel.a6 = e.a6 + r * e.a4 + r ^ 2 * e.a2 + r ^ 3
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
ValidModel.st_of_a1
[368, 1]
[369, 66]
simp only [rst_iso, Model.rst_iso, one_pow, mul_zero, one_mul]
R : Type u inst✝ : CommRing R e : ValidModel R s t : R ⊢ (rst_iso 0 s t e).toModel.a1 = e.a1 + 2 * s
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
ValidModel.st_of_a2
[371, 1]
[372, 99]
simp only [rst_iso, Model.rst_iso, one_pow, mul_zero, one_mul, add_zero, mul_assoc, ←pow_two s]
R : Type u inst✝ : CommRing R e : ValidModel R s t : R ⊢ (rst_iso 0 s t e).toModel.a2 = e.a2 - s * e.a1 - s ^ 2
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
ValidModel.st_of_a3
[374, 1]
[375, 97]
simp only [rst_iso, Model.rst_iso, one_pow, mul_zero, one_mul, add_zero, mul_assoc, zero_mul]
R : Type u inst✝ : CommRing R e : ValidModel R s t : R ⊢ (rst_iso 0 s t e).toModel.a3 = e.a3 + 2 * t
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
ValidModel.st_of_a4
[377, 1]
[379, 97]
simp only [rst_iso, Model.rst_iso, one_pow, mul_zero, one_mul, add_zero, mul_assoc, zero_mul]
R : Type u inst✝ : CommRing R e : ValidModel R s t : R ⊢ (rst_iso 0 s t e).toModel.a4 = e.a4 - s * e.a3 - t * e.a1 - 2 * s * t
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
ValidModel.st_of_a6
[381, 1]
[383, 63]
simp only [rst_iso, Model.rst_iso, one_pow, mul_zero, one_mul, add_zero, mul_assoc, ←pow_two t, zero_mul, mul_add, sub_sub]
R : Type u inst✝ : CommRing R e : ValidModel R s t : R ⊢ (rst_iso 0 s t e).toModel.a6 = e.a6 - t * e.a3 - t ^ 2
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
ValidModel.st_of_b8
[385, 1]
[387, 43]
rw [rst_iso, Model.rst_b8]
R : Type u inst✝ : CommRing R e : ValidModel R s t : R ⊢ Model.b8 (rst_iso 0 s t e).toModel = Model.b8 e.toModel
R : Type u inst✝ : CommRing R e : ValidModel R s t : R ⊢ Model.b8 e.toModel + 3 * 0 * Model.b6 e.toModel + 3 * 0 * 0 * Model.b4 e.toModel + 0 * 0 * 0 * Model.b2 e.toModel + 3 * 0 * 0 * 0 * 0 = Model.b8 e.toModel
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
ValidModel.st_of_b8
[385, 1]
[387, 43]
simp only [mul_zero, add_zero, zero_mul]
R : Type u inst✝ : CommRing R e : ValidModel R s t : R ⊢ Model.b8 e.toModel + 3 * 0 * Model.b6 e.toModel + 3 * 0 * 0 * Model.b4 e.toModel + 0 * 0 * 0 * Model.b2 e.toModel + 3 * 0 * 0 * 0 * 0 = Model.b8 e.toModel
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.discr_eq_zero_of_singular
[406, 1]
[411, 57]
rcases h with ⟨h₁, h₂, h₃⟩
K : Type u inst✝ : CommRing K e : Model K P : K × K h : is_singular_point e P ⊢ discr e = 0
case intro.intro K : Type u inst✝ : CommRing K e : Model K P : K × K h₁ : weierstrass e P = 0 h₂ : dweierstrass_dx e P = 0 h₃ : dweierstrass_dy e P = 0 ⊢ discr e = 0
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.discr_eq_zero_of_singular
[406, 1]
[411, 57]
rw [discr_in_jacobian_ideal, h₁, h₂, h₃, mul_zero, mul_zero, mul_zero, add_zero, add_zero, neg_eq_zero]
case intro.intro K : Type u inst✝ : CommRing K e : Model K P : K × K h₁ : weierstrass e P = 0 h₂ : dweierstrass_dx e P = 0 h₃ : dweierstrass_dy e P = 0 ⊢ discr e = 0
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.c4_zero_iff_a1_zero_of_char_two
[417, 1]
[426, 11]
have hchar' : (ringChar K : K) = 2 := by simp [h]
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 2 ⊢ c4 e = 0 ↔ e.a1 = 0
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 2 hchar' : ↑(ringChar K) = 2 ⊢ c4 e = 0 ↔ e.a1 = 0
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.c4_zero_iff_a1_zero_of_char_two
[417, 1]
[426, 11]
have hchar'' : (2 : K) = 0 := by simp [← hchar', ringChar.Nat.cast_ringChar]
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 2 hchar' : ↑(ringChar K) = 2 ⊢ c4 e = 0 ↔ e.a1 = 0
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 2 hchar' : ↑(ringChar K) = 2 hchar'' : 2 = 0 ⊢ c4 e = 0 ↔ e.a1 = 0
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.c4_zero_iff_a1_zero_of_char_two
[417, 1]
[426, 11]
rw [c4, b2, show (24 : K) = 2 * 12 by norm_num, show (4 : K) = 2 * 2 by norm_num, hchar'', ← pow_two]
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 2 hchar' : ↑(ringChar K) = 2 hchar'' : 2 = 0 ⊢ c4 e = 0 ↔ e.a1 = 0
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 2 hchar' : ↑(ringChar K) = 2 hchar'' : 2 = 0 ⊢ (e.a1 ^ 2 + 0 * 0 * e.a2) ^ 2 - 0 * 12 * b4 e = 0 ↔ e.a1 = 0
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.c4_zero_iff_a1_zero_of_char_two
[417, 1]
[426, 11]
simp only [mul_zero, zero_mul, add_zero, ← pow_mul, sub_zero]
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 2 hchar' : ↑(ringChar K) = 2 hchar'' : 2 = 0 ⊢ (e.a1 ^ 2 + 0 * 0 * e.a2) ^ 2 - 0 * 12 * b4 e = 0 ↔ e.a1 = 0
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 2 hchar' : ↑(ringChar K) = 2 hchar'' : 2 = 0 ⊢ e.a1 ^ (2 * 2) = 0 ↔ e.a1 = 0
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.c4_zero_iff_a1_zero_of_char_two
[417, 1]
[426, 11]
rw [pow_eq_zero_iff]
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 2 hchar' : ↑(ringChar K) = 2 hchar'' : 2 = 0 ⊢ e.a1 ^ (2 * 2) = 0 ↔ e.a1 = 0
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 2 hchar' : ↑(ringChar K) = 2 hchar'' : 2 = 0 ⊢ 0 < 2 * 2
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.c4_zero_iff_a1_zero_of_char_two
[417, 1]
[426, 11]
norm_num
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 2 hchar' : ↑(ringChar K) = 2 hchar'' : 2 = 0 ⊢ 0 < 2 * 2
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.c4_zero_iff_a1_zero_of_char_two
[417, 1]
[426, 11]
simp [h]
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 2 ⊢ ↑(ringChar K) = 2
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.c4_zero_iff_a1_zero_of_char_two
[417, 1]
[426, 11]
simp [← hchar', ringChar.Nat.cast_ringChar]
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 2 hchar' : ↑(ringChar K) = 2 ⊢ 2 = 0
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.c4_zero_iff_a1_zero_of_char_two
[417, 1]
[426, 11]
norm_num
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 2 hchar' : ↑(ringChar K) = 2 hchar'' : 2 = 0 ⊢ 24 = 2 * 12
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.c4_zero_iff_a1_zero_of_char_two
[417, 1]
[426, 11]
norm_num
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 2 hchar' : ↑(ringChar K) = 2 hchar'' : 2 = 0 ⊢ 4 = 2 * 2
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.c4_zero_iff_b2_zero_of_char_three
[428, 1]
[436, 11]
have hchar' : (ringChar K : K) = 3 := by simp [h]
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 3 ⊢ c4 e = 0 ↔ b2 e = 0
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 3 hchar' : ↑(ringChar K) = 3 ⊢ c4 e = 0 ↔ b2 e = 0
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.c4_zero_iff_b2_zero_of_char_three
[428, 1]
[436, 11]
have hchar'' : (3 : K) = 0 := by simp [← hchar', ringChar.Nat.cast_ringChar]
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 3 hchar' : ↑(ringChar K) = 3 ⊢ c4 e = 0 ↔ b2 e = 0
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 3 hchar' : ↑(ringChar K) = 3 hchar'' : 3 = 0 ⊢ c4 e = 0 ↔ b2 e = 0
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.c4_zero_iff_b2_zero_of_char_three
[428, 1]
[436, 11]
rw [c4, show (24 : K) = 3 * 8 by norm_num, hchar'']
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 3 hchar' : ↑(ringChar K) = 3 hchar'' : 3 = 0 ⊢ c4 e = 0 ↔ b2 e = 0
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 3 hchar' : ↑(ringChar K) = 3 hchar'' : 3 = 0 ⊢ b2 e ^ 2 - 0 * 8 * b4 e = 0 ↔ b2 e = 0
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.c4_zero_iff_b2_zero_of_char_three
[428, 1]
[436, 11]
simp only [mul_zero, zero_mul, add_zero, sub_zero]
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 3 hchar' : ↑(ringChar K) = 3 hchar'' : 3 = 0 ⊢ b2 e ^ 2 - 0 * 8 * b4 e = 0 ↔ b2 e = 0
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 3 hchar' : ↑(ringChar K) = 3 hchar'' : 3 = 0 ⊢ b2 e ^ 2 = 0 ↔ b2 e = 0
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.c4_zero_iff_b2_zero_of_char_three
[428, 1]
[436, 11]
rw [pow_eq_zero_iff]
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 3 hchar' : ↑(ringChar K) = 3 hchar'' : 3 = 0 ⊢ b2 e ^ 2 = 0 ↔ b2 e = 0
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 3 hchar' : ↑(ringChar K) = 3 hchar'' : 3 = 0 ⊢ 0 < 2
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.c4_zero_iff_b2_zero_of_char_three
[428, 1]
[436, 11]
norm_num
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 3 hchar' : ↑(ringChar K) = 3 hchar'' : 3 = 0 ⊢ 0 < 2
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.c4_zero_iff_b2_zero_of_char_three
[428, 1]
[436, 11]
simp [h]
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 3 ⊢ ↑(ringChar K) = 3
no goals
https://github.com/KisaraBlue/ec-tate-lean.git
b9d36a5b70bb0958bf9741ae6216a43b35c87ed4
ECTate/Algebra/EllipticCurve/Model.lean
Model.c4_zero_iff_b2_zero_of_char_three
[428, 1]
[436, 11]
simp [← hchar', ringChar.Nat.cast_ringChar]
K : Type u inst✝¹ : CommRing K inst✝ : IsDomain K e : Model K h : ringChar K = 3 hchar' : ↑(ringChar K) = 3 ⊢ 3 = 0
no goals