Theorems · Theorem · commutative algebra
Submodule.neg_toAddSubmonoid
∀ {R : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (S : Submodule R M),
(-S).toAddSubmonoid = -S.toAddSubmonoid- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- SemiringAddCommGroupModule
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- Submodulestatement and proof · cited by 7,192
- AddSubmonoidstatement · cited by 1,178
- Submodule.toAddSubmonoidstatement · cited by 162
- Submodule.pointwiseNegstatement · cited by 20
- AddSubmonoid.negstatement · cited by 16
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