Theorems · Theorem · linear algebra

LinearEquiv.map_mem_invtSubmodule_conj_iff

∀ {R : Type u_3} {M : Type u_4} {N : Type u_5} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [inst_3 : AddCommMonoid N] [inst_4 : Module R N] {f : Module.End R M} {e : M ≃ₗ[R] N} {p : Submodule R M},
  Submodule.map (↑e) p ∈ (e.conj f).invtSubmodule ↔ p ∈ f.invtSubmodule

Defined in

Mathlib.Algebra.Module.Submodule.Invariant

Cited by

1 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModule