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Theorems · Theorem · linear algebra

Submodule.prod_bot

∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {M' : Type u_8}
  [inst_3 : AddCommMonoid M'] [inst_4 : Module R M'], ⊥.prod ⊥ = ⊥
Defined in
Mathlib.LinearAlgebra.Span.Basic
Cited by
4 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Quot.sound
Assumes
SemiringAddCommMonoidModuleAddCommMonoidModule
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Around this declaration

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

LinearMap.ker_prod · cited by 4LinearMap.ker_prodSubmodule.ker_inl · cited by 1Submodule.ker_inlSubmodule.ker_inr · cited by 1Submodule.ker_inrLinearMap.ker_prodMap · cited by 1LinearMap.ker_prodMapModule · cited by 20661ModuleSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidSubmodule · cited by 7192SubmoduleBot.bot · cited by 4720Bot.botSubmodule.ext · cited by 204Submodule.extSubmodule.prod · cited by 55Submodule.prodSubmodule.prod_botCITED BYCITES

Cites7

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Cited by4

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