AffineSubspace.span_empty
∀ (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], affineSpan k ∅ = ⊥
The span of the empty set is ⊥.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Bot.botstatement · cited by 4,720
- AddTorsorstatement and proof · cited by 1,657
- AffineSubspacestatement · cited by 871
- affineSpanstatement · cited by 417
- GaloisInsertion.gcproof · cited by 137
- GaloisConnection.l_botproof · cited by 63
- AffineSubspace.giproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- AffineSubspace.map_spanproof · cited by 16
- AffineSubspace.nonempty_of_affineSpan_eq_topproof · cited by 3
- AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpanproof · cited by 2
- AffineBasis.nonemptyproof · cited by 2
- finrank_vectorSpan_insert_leproof · cited by 1
- affineSpan_prod_eqproof · cited by 1
- AffineMap.eqOn_affineSpanproof · cited by 1
- AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivialproof · cited by 0
- AffineIndependent.card_le_card_of_subset_affineSpanproof · cited by 0
- AffineIndependent.card_lt_card_of_affineSpan_lt_affineSpanproof · cited by 0