Theorems · Theorem · geometry

vectorSpan_insert_eq_vectorSpan

∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : AddTorsor V P] {p : P} {ps : Set P}, p ∈ affineSpan k ps → vectorSpan k (insert p ps) = vectorSpan k ps

If a point is in the affine span of a set, adding it to that set does not change the vector span.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs

Cited by

2 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor