AffineSubspace.vectorSpan_eq_top_of_affineSpan_eq_top
∀ (k : Type u_1) (V : Type u_2) (P : Type u_3) [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
[S : AddTorsor V P] {s : Set P}, affineSpan k s = ⊤ → vectorSpan k s = ⊤If the affine span of a set is ⊤, then the vector span of the same set is the ⊤.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement and proof · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- AddTorsorstatement and proof · cited by 1,657
- AffineSubspacestatement and proof · cited by 871
- affineSpanstatement and proof · cited by 417
- AffineSubspace.directionproof · cited by 339
- vectorSpanstatement · cited by 123
- direction_affineSpanproof · cited by 46
Cited by2
Results whose statement or proof uses this declaration.
- AffineIndependent.affineSpan_eq_top_iff_card_eq_finrank_add_oneproof · cited by 4
- AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonemptyproof · cited by 1