Theorems · Theorem · geometry

AffineMap.lineMap_lineMap_left

∀ {k : Type u_1} {V1 : Type u_2} {P1 : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V1] [inst_2 : Module k V1]
  [inst_3 : AddTorsor V1 P1] (p₀ p₁ : P1) (c d : k),
  (AffineMap.lineMap ((AffineMap.lineMap p₀ p₁) c) p₁) d = (AffineMap.lineMap p₀ p₁) (1 - (1 - d) * (1 - c))

Defined in: Mathlib.LinearAlgebra.AffineSpace.AffineMap
Cited by: 1 results in Mathlib
Foundations: Depth 49 from the axioms · uses propext, Quot.sound
Assumes: Ring AddCommGroup Module AddTorsor

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Cites9

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
AddCommGroupstatement and proof · cited by 12,871
Ringstatement and proof · cited by 7,463
AddTorsorstatement and proof · cited by 1,657
AffineMapstatement · cited by 674
AffineMap.lineMapstatement and proof · cited by 254
AffineMap.lineMap_apply_one_subproof · cited by 8
AffineMap.lineMap_lineMap_rightproof · cited by 3

Cited by1

Results whose statement or proof uses this declaration.

List.exists_map_eq_of_sorted_nonempty_iff_wbtwproof · cited by 2