Theorems · Theorem · order theory
CompleteAtomicBooleanAlgebra.eq_setOf_le_sSup_and_isAtom
Deprecated since 2026-07-09Use CompleteAtomicBooleanAlgebra.eq_setOfPred_le_sSup_and_isAtom instead.
∀ {α : Type u_4} [inst : CompleteAtomicBooleanAlgebra α] {S : Set α},
(∀ a ∈ S, IsAtom a) → S = {a | a ≤ sSup S ∧ IsAtom a}Alias of CompleteAtomicBooleanAlgebra.eq_setOfPred_le_sSup_and_isAtom.
- Defined in
- Mathlib.Order.Atoms
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteAtomicBooleanAlgebra
Around this declaration
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.ofPredstatement · cited by 6,101
- SupSet.sSupstatement · cited by 954
- IsAtomstatement · cited by 130
- CompleteAtomicBooleanAlgebrastatement · cited by 3
- CompleteAtomicBooleanAlgebra.eq_setOfPred_le_sSup_and_isAtomproof · cited by 1
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