Theorems · Definition · order theory
CompleteAtomicBooleanAlgebra.toSetOfIsAtom
{α : Type u_4} → [inst : CompleteAtomicBooleanAlgebra α] → α ≃o Set { a // IsAtom a }Representation theorem for complete atomic boolean algebras:
For a complete atomic Boolean algebra α, toSetOfIsAtom is an order isomorphism
between α and the set of subsets of its atoms.
- Defined in
- Mathlib.Order.Atoms
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteAtomicBooleanAlgebra
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- Setstatement and proof · cited by 53,352
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
- SupSet.sSupproof · cited by 954
- OrderIsostatement · cited by 874
- IsAtomstatement and proof · cited by 130
- CompleteAtomicBooleanAlgebrastatement and proof · cited by 3
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