Theorems · Theorem · algebraic geometry
WeierstrassCurve.Projective.negDblY_of_Z_eq_zero
∀ {R : Type r} [inst : CommRing R] {W' : WeierstrassCurve.Projective R} [NoZeroDivisors R] {P : Fin 3 → R},
W'.Equation P → P 2 = 0 → W'.negDblY P = -P 1 ^ 4- Cited by
- 1 results in Mathlib
- Foundations
- Depth 101 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
- WeierstrassCurve.a₃proof · cited by 210
- WeierstrassCurve.a₄proof · cited by 187
- WeierstrassCurve.a₆proof · cited by 153
- WeierstrassCurve.Projective.Equationstatement and proof · cited by 88
- WeierstrassCurve.Projective.negDblYstatement · cited by 14
- WeierstrassCurve.Projective.X_eq_zero_of_Z_eq_zeroproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Projective.dblY_of_Z_eq_zeroproof · cited by 1