affineIndependent_of_subsingleton
∀ (k : Type u_1) {V : Type u_2} {P : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
[inst_3 : AddTorsor V P] {ι : Type u_4} [Subsingleton ι] (p : ι → P), AffineIndependent k pA family with at most one point is affinely independent.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- Finsetproof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Finset.sumproof · cited by 5,195
- AddTorsorstatement and proof · cited by 1,657
- AffineIndependentstatement · cited by 144
- Finset.weightedVSubproof · cited by 51
- Fintype.eq_of_subsingleton_of_sum_eqproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- AffineIndependent.map'proof · cited by 1
- IsOpen.exists_subset_affineIndependent_span_eq_topproof · cited by 1
- exists_affineIndependentproof · cited by 1
- AffineIndependent.of_compproof · cited by 1