AffineSubspace.not_le_iff_exists
∀ {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] (s₁ s₂ : AffineSubspace k P), ¬s₁ ≤ s₂ ↔ ∃ p ∈ s₁, p ∉ s₂One subspace is not less than or equal to another if and only if it has a point not in the second subspace.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- AddTorsorstatement and proof · cited by 1,657
- AffineSubspacestatement and proof · cited by 871
- Set.not_subsetproof · cited by 31
Cited by1
Results whose statement or proof uses this declaration.
- AffineSubspace.lt_iff_le_and_existsproof · cited by 1