Theorems · Theorem · linear algebra

Module.eq_of_mapsTo_reflection_of_mem

∀ {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] {Φ : Set M},
  Φ.Finite →
    f x = 2 →
      g y = 2 →
        g x = 2 →
          f y = 2 →
            Set.MapsTo (⇑(Module.preReflection x f)) Φ Φ → Set.MapsTo (⇑(Module.preReflection y g)) Φ Φ → y ∈ Φ → x = y

Defined in

Mathlib.LinearAlgebra.Reflection

Cited by

2 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleIsAddTorsionFree