Theorems · Theorem · order theory
IsAtom.le_sSup
∀ {α : Type u_2} [inst : Order.Frame α] {s : Set α} {a : α}, IsAtom a → (a ≤ sSup s ↔ ∃ b ∈ s, a ≤ b)- Defined in
- Mathlib.Order.Atoms
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, 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.
- Setstatement and proof · cited by 53,352
- Set.Elemproof · cited by 7,166
- SupSet.sSupstatement · cited by 954
- IsAtomstatement and proof · cited by 130
- Order.Framestatement and proof · cited by 88
- sSup_eq_iSup'proof · cited by 38
- IsAtom.le_iSupproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CompleteAtomicBooleanAlgebra.eq_setOfPred_le_sSup_and_isAtomproof · cited by 1