Theorems · Theorem · geometry

AffineMap.homothety_eq_lineMap

∀ {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 : P1) (r : k) (p : P1),
  (AffineMap.homothety c r) p = (AffineMap.lineMap c p) r

Defined in: Mathlib.LinearAlgebra.AffineSpace.AffineMap
Cited by: 4 results in Mathlib
Foundations: Depth 45 from the axioms · uses propext, Quot.sound
Assumes: CommRing AddCommGroup AddTorsor Module

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Cites8

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

DFunLike.coestatement · 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.lineMapstatement · cited by 254
AffineMap.homothetystatement · cited by 51

Cited by4

Results whose statement or proof uses this declaration.

Convex.closure_subset_image_homothety_interior_of_one_ltproof · cited by 2
dist_homothety_selfproof · cited by 2
AffineMap.homothety_memproof · cited by 1
Finset.homothety_affineCombinationproof · cited by 1