Theorems · Theorem · algebraic geometry
WeierstrassCurve.Affine.CoordinateRing.smul_basis_eq_zero
∀ {R : Type r} [inst : CommRing R] {W' : WeierstrassCurve.Affine R} {p q : Polynomial R},
p • 1 + q • (WeierstrassCurve.Affine.CoordinateRing.mk W') Polynomial.X = 0 → p = 0 ∧ q = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 134 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Finset.sumproof · cited by 5,195
- Finset.univproof · cited by 3,473
- Polynomial.Xstatement and proof · cited by 1,639
- Matrix.vecConsproof · cited by 852
- Matrix.vecEmptyproof · cited by 832
- WeierstrassCurve.Affinestatement and proof · cited by 174
- WeierstrassCurve.Affine.polynomialstatement · cited by 61
- Module.Basis.linearIndependentproof · cited by 54
Cited by1
Results whose statement or proof uses this declaration.
- WeierstrassCurve.Affine.CoordinateRing.map_injectiveproof · cited by 0