Theorems · Theorem · geometry

AffineMap.homothety_mul

∀ {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) (r₁ r₂ : k),
  AffineMap.homothety c (r₁ * r₂) = (AffineMap.homothety c r₁).comp (AffineMap.homothety c r₂)

Defined in: Mathlib.LinearAlgebra.AffineSpace.AffineMap
Cited by: 0 results in Mathlib
Foundations: Depth 46 from the axioms · uses propext, Quot.sound
Assumes: CommRing AddCommGroup AddTorsor Module

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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 · cited by 51
AffineMap.compstatement · cited by 20
AffineMap.extproof · cited by 19
AffineMap.homothety_mul_applyproof · cited by 2

Cited by1

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AffineMap.homothetyHomproof · cited by 2