Theorems · Theorem · algebraic geometry
WeierstrassCurve.Projective.Y_ne_zero_of_Z_eq_zero
∀ {R : Type r} [inst : CommRing R] {W' : WeierstrassCurve.Projective R} [NoZeroDivisors R] {P : Fin 3 → R},
W'.Nonsingular P → P 2 = 0 → P 1 ≠ 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 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.
Cites15
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
- add_zeroproof · cited by 2,707
- MulZeroClass.mul_zeroproof · cited by 2,091
- sub_zeroproof · cited by 938
- NoZeroDivisorsstatement and proof · cited by 545
- MonoidWithZeroproof · cited by 456
- zero_powproof · cited by 361
- WeierstrassCurve.a₁proof · cited by 272
- two_ne_zeroproof · cited by 251
- WeierstrassCurve.Projectivestatement and proof · cited by 244
- WeierstrassCurve.a₂proof · cited by 216
- WeierstrassCurve.Projective.Equationproof · cited by 88
Cited by1
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Projective.isUnit_Y_of_Z_eq_zeroproof · cited by 8