Theorems · Theorem · order theory
IsCompactlyGenerated.BooleanGenerators.isAtom
∀ {α : Type u_1} [inst : CompleteLattice α] {S : Set α}, IsCompactlyGenerated.BooleanGenerators S → ∀ I ∈ S, IsAtom IThe elements in a collection of Boolean generators are all atoms.
- Defined in
- Mathlib.Order.BooleanGenerators
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- CompleteLatticestatement and proof · cited by 1,048
- IsAtomstatement · cited by 130
- IsCompactlyGenerated.BooleanGeneratorsstatement and proof · cited by 11
Cited by6
Results whose statement or proof uses this declaration.
- IsCompactlyGenerated.BooleanGenerators.mem_of_isAtom_of_le_sSup_atomsproof · cited by 3
- IsCompactlyGenerated.BooleanGenerators.monoproof · cited by 2
- IsCompactlyGenerated.BooleanGenerators.isAtomistic_of_sSup_eq_topproof · cited by 1
- IsCompactlyGenerated.BooleanGenerators.sSup_le_sSup_iff_of_atomsproof · cited by 0
- IsCompactlyGenerated.BooleanGenerators.eq_atoms_of_sSup_eq_topproof · cited by 0
- IsCompactlyGenerated.BooleanGenerators.sSup_interproof · cited by 0