Theorems · Inductive type · order theory
CompleteAtomicBooleanAlgebra
Type u → Type u
A complete atomic Boolean algebra is a complete Boolean algebra that is also completely distributive. We take iSup_iInf_eq as the definition here, and prove later on that this implies atomicity.
- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 0 from the axioms · uses no axioms
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Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by14
Results whose statement or proof uses this declaration.
- CompleteAtomicBooleanAlgebra.eq_setOfPred_le_sSup_and_isAtomstatement and proof · cited by 1
- CompleteBooleanAlgebra.toCompleteAtomicBooleanAlgebrastatement · cited by 0
- CompleteAtomicBooleanAlgebra.mk.noConfusionstatement · cited by 0
- Equiv.completeAtomicBooleanAlgebrastatement and proof · cited by 0
- CompleteAtomicBooleanAlgebra.casesOnstatement and proof · cited by 0
- CompleteAtomicBooleanAlgebra.ctorIdxstatement and proof · cited by 0
- CompleteAtomicBooleanAlgebra.eq_setOf_le_sSup_and_isAtomstatement · cited by 0
- CompleteAtomicBooleanAlgebra.iInf_iSup_eqstatement and proof · cited by 0
- CompleteAtomicBooleanAlgebra.recOnstatement and proof · cited by 0
- CompleteAtomicBooleanAlgebra.noConfusionstatement and proof · cited by 0
- CompleteAtomicBooleanAlgebra.noConfusionTypestatement and proof · cited by 0
- Function.Injective.completeAtomicBooleanAlgebrastatement and proof · cited by 0