Mathlib Map

Theorems · Definition · commutative algebra

Submodule.negOrderIso

{R : Type u_2} →
  {M : Type u_3} →
    [inst : Semiring R] → [inst_1 : AddCommGroup M] → [inst_2 : Module R M] → Submodule R M ≃o Submodule R M

Submodule.pointwiseNeg as an order isomorphism.

Defined in
Mathlib.Algebra.Module.Submodule.Pointwise
Cited by
3 results in Mathlib
Foundations
Depth 28 from the axioms · uses propext, Quot.sound
Assumes
SemiringAddCommGroupModule
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Submodule.neg_sup · cited by 0Submodule.neg_supSubmodule.neg_iInf · cited by 0Submodule.neg_iInfSubmodule.neg_iSup · cited by 0Submodule.neg_iSupModule · cited by 20661ModuleSemiring · cited by 13802SemiringAddCommGroup · cited by 12871AddCommGroupEquiv · cited by 8337EquivSubmodule · cited by 7192SubmoduleOrderIso · cited by 874OrderIsoEquiv.neg · cited by 53Equiv.negSubmodule.neg_le_neg · cited by 0Submodule.neg_le_negSubmodule.negOrderIsoCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.