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Theorems · Theorem · linear algebra

LinearMap.ker_id

∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],
  LinearMap.id.ker = ⊥
Defined in
Mathlib.Algebra.Module.Submodule.Ker
Cited by
1 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Quot.sound
Assumes
SemiringAddCommMonoidModule
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Around this declaration

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

LinearMap.id_separatingLeft · cited by 2LinearMap.id_separatingLe…Module · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidSubmodule · cited by 7192SubmoduleBot.bot · cited by 4720Bot.botLinearMap.ker · cited by 848LinearMap.kerLinearMap.id · cited by 625LinearMap.idLinearMap.ker_idCITED BYCITES

Cites8

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Cited by1

Results whose statement or proof uses this declaration.