Theorems · Theorem · order theory
sup_lt_of_lt_sdiff_left
∀ {α : Type u} {x y z : α} [inst : GeneralizedBooleanAlgebra α], y < z \ x → x ≤ z → x ⊔ y < z- Defined in
- Mathlib.Order.BooleanAlgebra.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 52 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LE.le.transproof · cited by 3,151
- LT.lt.leproof · cited by 2,189
- LT.lt.not_geproof · cited by 305
- GeneralizedBooleanAlgebrastatement and proof · cited by 204
- sdiff_leproof · cited by 36
- LE.le.lt_of_not_geproof · cited by 21
- sup_le_sup_leftproof · cited by 20
- sdiff_idemproof · cited by 12
- sup_sdiff_cancel_rightproof · cited by 6
- sdiff_le_sdiff_of_sup_le_sup_leftproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Finset.Ico_eq_image_ssubsetsproof · cited by 0