Theorems · Theorem · geometry

AffineSubspace.mem_inf_iff

∀ {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] (p : P) (s₁ s₂ : AffineSubspace k P), p ∈ s₁ ⊓ s₂ ↔ p ∈ s₁ ∧ p ∈ s₂

A point is in the inf of two affine subspaces if and only if it is in both of them.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs

Cited by

4 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor