Theorems · Theorem · convex and discrete geometry

Convexity.convexCombPair.congr_simp

∀ {R : Type u_1} {M : Type u_3} [inst : PartialOrder R] [inst_1 : Semiring R] [inst_2 : IsStrictOrderedRing R]
  [inst_3 : Convexity.ConvexSpace R M] (s s_1 : R) (e_s : s = s_1) (t t_1 : R) (e_t : t = t_1) (hs : 0 ≤ s) (ht : 0 ≤ t)
  (hst : s + t = 1) (x x_1 : M),
  x = x_1 →
    ∀ (y y_1 : M), y = y_1 → Convexity.convexCombPair s t hs ht hst x y = Convexity.convexCombPair s_1 t_1 ⋯ ⋯ ⋯ x_1 y_1

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Defs

Cited by

10 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderSemiringIsStrictOrderedRingConvexity.ConvexSpace