AffineSubspace.parallel_bot_iff_eq_bot
∀ {k : Type u_1} {V : Type u_2} {P : Type u_4} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
[inst_3 : AddTorsor V P] {s : AffineSubspace k P}, s.Parallel ⊥ ↔ s = ⊥- Cited by
- 2 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Ringstatement and proof · cited by 7,463
- Bot.botstatement and proof · cited by 4,720
- AddTorsorstatement and proof · cited by 1,657
- AffineSubspacestatement and proof · cited by 871
- AffineSubspace.mapproof · cited by 78
- AffineEquiv.toAffineMapproof · cited by 65
- AffineEquiv.constVAddproof · cited by 30
- AffineSubspace.Parallelstatement and proof · cited by 19
- AffineSubspace.Parallel.reflproof · cited by 2
- AffineSubspace.map_eq_bot_iffproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- AffineSubspace.parallel_iff_direction_eq_and_eq_bot_iff_eq_botproof · cited by 1
- AffineSubspace.bot_parallel_iff_eq_botproof · cited by 1