Theorems · Theorem · algebraic geometry
WeierstrassCurve.Projective.nonsingular_smul
∀ {R : Type r} [inst : CommRing R] {W' : WeierstrassCurve.Projective R} (P : Fin 3 → R) {u : R},
IsUnit u → (W'.Nonsingular (u • P) ↔ W'.Nonsingular P)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Units.valproof · cited by 1,966
- Nat.cast_zeroproof · cited by 1,870
- IsUnitstatement and proof · cited by 1,602
- one_smulproof · cited by 1,374
- smul_smulproof · cited by 360
- WeierstrassCurve.a₁proof · cited by 272
- IsUnit.unitproof · cited by 252
- WeierstrassCurve.Projectivestatement and proof · cited by 244
- WeierstrassCurve.a₂proof · cited by 216
- WeierstrassCurve.a₃proof · cited by 210
- WeierstrassCurve.a₄proof · cited by 187
Cited by5
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Projective.Point.toAffine_smulproof · cited by 3
- WeierstrassCurve.Projective.nonsingular_negproof · cited by 2
- WeierstrassCurve.Projective.nonsingular_of_equivproof · cited by 1
- WeierstrassCurve.Projective.nonsingular_addproof · cited by 1
- WeierstrassCurve.Projective.Point.toAffine_negproof · cited by 1