Theorems · Theorem · algebraic geometry
WeierstrassCurve.Projective.X_eq_zero_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 → P 0 = 0- Cited by
- 12 results in Mathlib
- Foundations
- Depth 100 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.
Cites6
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
- NoZeroDivisorsstatement and proof · cited by 545
- WeierstrassCurve.Projectivestatement and proof · cited by 244
- WeierstrassCurve.Projective.Equationstatement and proof · cited by 88
- eq_zero_of_pow_eq_zeroproof · cited by 30
- WeierstrassCurve.Projective.equation_of_Z_eq_zeroproof · cited by 1
Cited by12
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Projective.neg_of_Z_eq_zeroproof · cited by 3
- WeierstrassCurve.Projective.equiv_of_Z_eq_zeroproof · cited by 3
- WeierstrassCurve.Projective.addZ_of_Z_eq_zero_leftproof · cited by 2
- WeierstrassCurve.Projective.addZ_of_Z_eq_zero_rightproof · cited by 2
- WeierstrassCurve.Projective.addX_of_Z_eq_zero_leftproof · cited by 2
- WeierstrassCurve.Projective.addX_of_Z_eq_zero_rightproof · cited by 2
- WeierstrassCurve.Projective.dblX_of_Z_eq_zeroproof · cited by 2
- WeierstrassCurve.Projective.negAddY_of_Z_eq_zero_leftproof · cited by 1
- WeierstrassCurve.Projective.negAddY_of_Z_eq_zero_rightproof · cited by 1
- WeierstrassCurve.Projective.Y_ne_zero_of_Z_eq_zeroproof · cited by 1
- WeierstrassCurve.Projective.negDblY_of_Z_eq_zeroproof · cited by 1
- WeierstrassCurve.Projective.negY_of_Z_eq_zeroproof · cited by 1