Theorems · Theorem · order theory
IsCompactlyGenerated.BooleanGenerators.mono
∀ {α : Type u_1} [inst : CompleteLattice α] {S : Set α},
IsCompactlyGenerated.BooleanGenerators S → ∀ {T : Set α}, T ⊆ S → IsCompactlyGenerated.BooleanGenerators T- Defined in
- Mathlib.Order.BooleanGenerators
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- CompleteLatticestatement and proof · cited by 1,048
- le_transproof · cited by 985
- IsCompactlyGenerated.BooleanGeneratorsstatement and proof · cited by 11
- IsCompactlyGenerated.BooleanGenerators.isAtomproof · cited by 6
- IsCompactlyGenerated.BooleanGenerators.finitelyAtomisticproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- IsCompactlyGenerated.BooleanGenerators.sSup_le_sSup_iff_of_atomsproof · cited by 0
- IsCompactlyGenerated.BooleanGenerators.sSup_interproof · cited by 0