Collinear.subset
∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : DivisionRing k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
[inst_3 : AddTorsor V P] {s₁ s₂ : Set P}, s₁ ⊆ s₂ → Collinear k s₂ → Collinear k s₁A subset of a collinear set is collinear.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- LE.le.transproof · cited by 3,151
- AddTorsorstatement and proof · cited by 1,657
- DivisionRingstatement and proof · cited by 1,062
- Collinearstatement and proof · cited by 79
- Submodule.rank_monoproof · cited by 11
- vectorSpan_monoproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- affineIndependent_of_affineIndependent_collinear_neproof · cited by 1
- collinear_insert_insert_insert_left_of_mem_affineSpan_pairproof · cited by 1
- collinear_triple_of_mem_affineSpan_pairproof · cited by 0