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Theorems · Theorem · commutative algebra

Submodule.neg_le_neg

∀ {R : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  {S T : Submodule R M}, -S ≤ -T ↔ S ≤ T
Defined in
Mathlib.Algebra.Module.Submodule.Pointwise
Cited by
0 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Quot.sound
Assumes
SemiringAddCommGroupModule
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Around this declaration

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Submodule.negOrderIso · cited by 3Submodule.negOrderIsoModule · cited by 20661ModuleSemiring · cited by 13802SemiringAddCommGroup · cited by 12871AddCommGroupSubmodule · cited by 7192SubmoduleSetLike.coe_subset_coe · cited by 53SetLike.coe_subset_coeSubmodule.pointwiseNeg · cited by 20Submodule.pointwiseNegSet.neg_subset_neg · cited by 5Set.neg_subset_negSubmodule.neg_le_negCITED BYCITES

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Cited by1

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