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Theorems · Theorem · commutative algebra

Submodule.IsPrincipal.generator.congr_simp

∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  (S S_1 : Submodule R M) (e_S : S = S_1) [inst_3 : S.IsPrincipal],
  Submodule.IsPrincipal.generator S = Submodule.IsPrincipal.generator S_1
Defined in
Mathlib.RingTheory.Ideal.Prod
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Foundations
Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringAddCommMonoidModuleSubmodule.IsPrincipal
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Module · cited by 20661ModuleSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidSubmodule · cited by 7192SubmoduleSubmodule.IsPrincipal · cited by 129Submodule.IsPrincipalSubmodule.IsPrincipal.generator · cited by 56IsPrincipal.generatorgenerator.congr_simpCITED BYCITES

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