Theorems · Theorem · linear algebra

Module.infinite_range_reflection_reflection_iterate_iff

∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {x : M}
  {f : Module.Dual R M} {y : M} {g : Module.Dual R M} [IsAddTorsionFree M] (hfx : f x = 2) (hgy : g y = 2),
  f y * g x = 4 →
    ((Set.range fun n => (⇑(Module.reflection hgy ≪≫ₗ Module.reflection hfx))^[n] y).Infinite ↔ f y • x ≠ 2 • y)

Defined in

Mathlib.LinearAlgebra.Reflection

Cited by

2 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleIsAddTorsionFree