Theorems · Theorem · algebraic geometry
WeierstrassCurve.Projective.addX_of_X_eq
∀ {R : Type r} [inst : CommRing R] {W' : WeierstrassCurve.Projective R} [NoZeroDivisors R] {P Q : Fin 3 → R},
W'.Equation P → W'.Equation Q → P 2 ≠ 0 → Q 2 ≠ 0 → P 0 * Q 2 = Q 0 * P 2 → W'.addX P Q = 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingNoZeroDivisors
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Nat.cast_zeroproof · cited by 1,870
- NoZeroDivisorsstatement and proof · cited by 545
- WeierstrassCurve.a₁proof · cited by 272
- WeierstrassCurve.Projectivestatement and proof · cited by 244
- WeierstrassCurve.a₂proof · cited by 216
- pow_ne_zeroproof · cited by 208
- mul_ne_zeroproof · cited by 178
- WeierstrassCurve.Projective.Equationstatement and proof · cited by 88
- WeierstrassCurve.Projective.addXstatement · cited by 21
- eq_zero_of_ne_zero_of_mul_right_eq_zeroproof · cited by 7
- WeierstrassCurve.Projective.addX_eq'proof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Projective.addXYZ_of_X_eqproof · cited by 1
- WeierstrassCurve.Projective.addY_of_X_eq'proof · cited by 1