Theorems · Theorem · commutative algebra

Submodule.smithNormalFormCoeffs.congr_simp

∀ {ι : Type u_1} {R : Type u_2} [inst : CommRing R] {M : Type u_3} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [inst_3 : IsDomain R] [inst_4 : IsPrincipalIdealRing R] {N N_1 : Submodule R M} (e_N : N = N_1) [inst_5 : Finite ι]
  (b b_1 : Module.Basis ι R M),
  b = b_1 →
    ∀ (h : Module.finrank R ↥N = Module.finrank R M) (a a_1 : ι),
      a = a_1 → Submodule.smithNormalFormCoeffs b h a = Submodule.smithNormalFormCoeffs b_1 ⋯ a_1

Defined in

Mathlib.LinearAlgebra.FreeModule.PID

Cited by

0 results in Mathlib

Foundations

Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleIsDomainIsPrincipalIdealRingFinite