vectorSpan_def
∀ (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] (s : Set P), vectorSpan k s = Submodule.span k (s -ᵥ s)The definition of vectorSpan, for rewriting.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- AddTorsorstatement and proof · cited by 1,657
- Submodule.spanstatement · cited by 1,504
- VSub.vsubstatement · cited by 817
- vectorSpanstatement · cited by 123
Cited by7
Results whose statement or proof uses this declaration.
- vectorSpan_eq_span_vsub_set_rightproof · cited by 7
- vectorSpan_emptyproof · cited by 5
- vectorSpan_eq_span_vsub_set_leftproof · cited by 4
- AffineSubspace.direction_botproof · cited by 3
- vectorSpan_prod_eqproof · cited by 2
- AffineSubspace.direction_supproof · cited by 2
- affineSpan_insert_zeroproof · cited by 1