vectorSpan_eq_span_vsub_set_left
∀ (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} {p : P}, p ∈ s → vectorSpan k s = Submodule.span k ((fun x => p -ᵥ x) '' s)The vectorSpan is the span of the pairwise subtractions with a given point on the left.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- SetLike.coeproof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- Set.imagestatement and proof · cited by 5,609
- le_antisymmproof · cited by 2,068
- AddTorsorstatement and proof · cited by 1,657
- Submodule.spanstatement and proof · cited by 1,504
- VSub.vsubstatement and proof · cited by 817
- SetLike.mem_coeproof · cited by 302
Cited by4
Results whose statement or proof uses this declaration.
- vectorSpan_image_eq_span_vsub_set_left_neproof · cited by 3
- vectorSpan_pairproof · cited by 3
- vectorSpan_eq_span_vsub_set_left_neproof · cited by 1
- vectorSpan_range_eq_span_range_vsub_leftproof · cited by 0