Theorems · Theorem · geometry

AffineSubspace.direction_sInf_of_mem

∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [S : AddTorsor V P] (t : Set (AffineSubspace k P)) (p : P),
  (∀ s ∈ t, p ∈ s) → (sInf t).direction = ⨅ s ∈ t, s.direction

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs

Cited by

2 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor