Theorems · Theorem · geometry

Affine.Triangle.prod_eq_prod_one_sub_of_mem_line_point_lineMap

∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : CommRing k] [NoZeroDivisors k] [inst_2 : AddCommGroup V]
  [inst_3 : Module k V] [inst_4 : AddTorsor V P] {t : Affine.Triangle k P} {r : Fin 3 → k} {p' : P},
  (∀ (i : Fin 3), p' ∈ line[k, t.points i, (AffineMap.lineMap (t.points (i + 1)) (t.points (i + 2))) (r i)]) →
    ∏ i, r i = ∏ i, (1 - r i)

Ceva's theorem for a triangle, expressed in terms of multiplying weights.

Defined in: Mathlib.LinearAlgebra.AffineSpace.Ceva
Cited by: 2 results in Mathlib
Foundations: Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing NoZeroDivisors AddCommGroup Module AddTorsor

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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
Setstatement · cited by 53,352
Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
Finsetproof · cited by 13,712
AddCommGroupstatement and proof · cited by 12,871
Set.Elemproof · cited by 7,166
Finset.sumproof · cited by 5,195
Set.univproof · cited by 3,945
mul_oneproof · cited by 3,885
Finset.univstatement and proof · cited by 3,473
Compl.complproof · cited by 2,925

Cited by2

Results whose statement or proof uses this declaration.

Affine.Triangle.prod_dist_eq_prod_dist_of_mem_line_of_mem_lineproof · cited by 1
Affine.Triangle.prod_div_one_sub_eq_one_of_mem_line_point_lineMapproof · cited by 0