Theorems · Theorem · algebraic geometry
WeierstrassCurve.Projective.dblU_ne_zero_of_Y_eq
∀ {F : Type u} [inst : Field F] {W : WeierstrassCurve.Projective F} {P Q : Fin 3 → F},
W.Nonsingular P →
P 2 ≠ 0 → 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 → W.dblU P ≠ 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.Projectivestatement and proof · cited by 244
- pow_ne_zeroproof · cited by 208
- WeierstrassCurve.Projective.negYstatement and proof · cited by 56
- WeierstrassCurve.Projective.Nonsingularstatement and proof · cited by 37
- div_ne_zeroproof · cited by 29
- WeierstrassCurve.Projective.dblUstatement · cited by 11
- WeierstrassCurve.Projective.Y_eq_negY_of_Y_eqproof · cited by 4
- WeierstrassCurve.Projective.nonsingular_iff_of_Y_eq_negYproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Projective.isUnit_dblU_of_Y_eqproof · cited by 3