Theorems · Theorem · algebraic geometry
WeierstrassCurve.Affine.slope_of_X_ne
∀ {F : Type u} [inst : Field F] {W : WeierstrassCurve.Affine F} [inst_1 : DecidableEq F] {x₁ x₂ y₁ y₂ : F},
x₁ ≠ x₂ → W.slope x₁ x₂ y₁ y₂ = (y₁ - y₂) / (x₁ - x₂)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Quot.sound
- Assumes
- FieldDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- WeierstrassCurve.Affinestatement and proof · cited by 174
- WeierstrassCurve.Affine.slopestatement · cited by 54
Cited by6
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Affine.nonsingular_negAddproof · cited by 4
- WeierstrassCurve.Affine.addPolynomial_slopeproof · cited by 3
- WeierstrassCurve.Affine.map_slopeproof · cited by 1
- WeierstrassCurve.Affine.cyclic_sum_Y_mul_X_sub_Xproof · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.XYIdeal_eq₂proof · cited by 1
- WeierstrassCurve.Affine.addX_eq_addX_negY_subproof · cited by 0