AffineSubspace.nonempty_iff_ne_bot
∀ {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] (Q : AffineSubspace k P), (↑Q).Nonempty ↔ Q ≠ ⊥- Cited by
- 4 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- SetLike.coestatement · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Bot.botstatement and proof · cited by 4,720
- Set.Nonemptystatement · cited by 2,627
- AddTorsorstatement and proof · cited by 1,657
- AffineSubspacestatement and proof · cited by 871
- Set.nonempty_iff_ne_emptyproof · cited by 96
- AffineSubspace.coe_eq_bot_iffproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- AffineSubspace.eq_bot_or_nonemptyproof · cited by 5
- affineSpan_eq_botproof · cited by 2
- AffineSubspace.parallel_iff_direction_eq_and_eq_bot_iff_eq_botproof · cited by 1
- AffineSubspace.perpBisector_ne_botproof · cited by 0