Theorems · Theorem · geometry

affineSpan_pair_le_of_right_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]
  [inst_3 : AddTorsor V P] {p₁ p₂ p₃ : P}, p₁ ∈ line[k, p₂, p₃] → line[k, p₂, p₁] ≤ line[k, p₂, p₃]

One line is contained in another differing in the second point if the second point of the first line is contained in the second line.

Defined in

Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs

Cited by

1 results in Mathlib

Foundations

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

Assumes

RingAddCommGroupModuleAddTorsor