Theorems · Theorem · order theory
sdiff_lt
∀ {α : Type u} {x y : α} [inst : GeneralizedBooleanAlgebra α], y ≤ x → y ≠ ⊥ → x \ y < x- Defined in
- Mathlib.Order.BooleanAlgebra.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GeneralizedBooleanAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement and proof · cited by 4,720
- GeneralizedBooleanAlgebrastatement and proof · cited by 204
- LE.le.lt_of_neproof · cited by 116
- disjoint_iffproof · cited by 76
- inf_eq_rightproof · cited by 64
- sdiff_leproof · cited by 36
- sdiff_eq_leftproof · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- CovBy.exists_set_sdiff_singletonproof · cited by 2
- Set.sdiff_singleton_covByproof · cited by 1