Theorems · Theorem · linear algebra
Submodule.span_neg_eq_neg
∀ {R : Type u_8} {M : Type u_9} [inst : Semiring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (s : Set M),
Submodule.span R (-s) = -Submodule.span R s- Defined in
- Mathlib.LinearAlgebra.Span.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- SetLike.coeproof · cited by 8,199
- Submodulestatement · cited by 7,192
- le_antisymmproof · cited by 2,068
- Submodule.spanstatement and proof · cited by 1,504
- neg_negproof · cited by 960
- Submodule.subset_spanproof · cited by 234
- Set.negstatement · cited by 168
- Submodule.span_leproof · cited by 164
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.span_negproof · cited by 1