Theorems · Theorem · geometry

AffineEquiv.symm_apply_eq

∀ {k : Type u_1} {P₁ : Type u_2} {P₂ : Type u_3} {V₁ : Type u_6} {V₂ : Type u_7} [inst : Ring k]
  [inst_1 : AddCommGroup V₁] [inst_2 : AddCommGroup V₂] [inst_3 : Module k V₁] [inst_4 : Module k V₂]
  [inst_5 : AddTorsor V₁ P₁] [inst_6 : AddTorsor V₂ P₂] (e : P₁ ≃ᵃ[k] P₂) {p₁ : P₂} {p₂ : P₁},
  e.symm p₁ = p₂ ↔ p₁ = e p₂

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineEquiv

Cited by

2 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupAddCommGroupModuleModuleAddTorsorAddTorsor