Theorems · Theorem · order theory
himp_eq_sSup
∀ {α : Type u} [inst : Order.Frame α] {a b : α}, a ⇨ b = sSup {w | w ⊓ a ≤ b}- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
- Assumes
- Order.Frame
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.
- Set.ofPredstatement · cited by 6,101
- SupSet.sSupstatement · cited by 954
- HImp.himpstatement · cited by 153
- Order.Framestatement and proof · cited by 88
- IsGreatest.isLUBproof · cited by 25
- IsLUB.sSup_eqproof · cited by 17
- isGreatest_himpproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- TopologicalSpace.Opens.mem_himpproof · cited by 0
- himp_le_iffproof · cited by 0