Theorems · Theorem · geometry

AffineSubspace.vadd_mem_of_mem_direction

∀ {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] {s : AffineSubspace k P} {v : V}, v ∈ s.direction → ∀ {p : P}, p ∈ s → v +ᵥ p ∈ s

Adding a vector in the direction to a point in the subspace produces a point in the subspace.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs

Cited by

17 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor