Theorems · Theorem · geometry

AffineMap.homothety_eq_iff_of_mul_eq_one

∀ {k : Type u_2} {V1 : Type u_3} {P1 : Type u_4} [inst : CommRing k] [inst_1 : AddCommGroup V1]
  [inst_2 : AddTorsor V1 P1] [inst_3 : Module k V1] {c p q : P1} {r₁ r₂ : k},
  r₁ * r₂ = 1 → ((AffineMap.homothety c r₁) p = q ↔ (AffineMap.homothety c r₂) q = p)

Defined in: Mathlib.LinearAlgebra.AffineSpace.AffineMap
Cited by: 1 results in Mathlib
Foundations: Depth 46 from the axioms · uses propext, Quot.sound
Assumes: CommRing AddCommGroup AddTorsor Module

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
AddTorsorstatement and proof · cited by 1,657
AffineMapstatement · cited by 674
AffineMap.homothetystatement and proof · cited by 51
mul_eq_one_commproof · cited by 5
AffineMap.homothety_oneproof · cited by 3
AffineMap.homothety_mul_applyproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

Affine.Simplex.closedInterior_inter_shift_eq_homothetyproof · cited by 0