Theorems · Theorem · algebraic geometry
WeierstrassCurve.Projective.Y_eq_negY_of_Y_eq
∀ {R : Type r} [inst : CommRing R] {W' : WeierstrassCurve.Projective R} [NoZeroDivisors R] {P Q : Fin 3 → R},
Q 2 ≠ 0 → P 0 * Q 2 = Q 0 * P 2 → P 1 * Q 2 = Q 1 * P 2 → P 1 * Q 2 = W'.negY Q * P 2 → P 1 = W'.negY P- Cited by
- 4 results in Mathlib
- Foundations
- Depth 49 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.
Cites7
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.Projectivestatement and proof · cited by 244
- WeierstrassCurve.Projective.negYstatement and proof · cited by 56
- mul_left_injective₀proof · cited by 22
- WeierstrassCurve.Projective.Y_sub_Y_add_Y_sub_negYproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Projective.negDblY_of_Y_eq'proof · cited by 2
- WeierstrassCurve.Projective.dblZ_of_Y_eqproof · cited by 2
- WeierstrassCurve.Projective.dblX_of_Y_eqproof · cited by 2
- WeierstrassCurve.Projective.dblU_ne_zero_of_Y_eqproof · cited by 1