Theorems · Theorem · order theory
CompleteLattice.wellFoundedGT_iff_isSupFiniteCompact
∀ (α : Type u_2) [inst : CompleteLattice α], WellFoundedGT α ↔ CompleteLattice.IsSupFiniteCompact α
- Defined in
- Mathlib.Order.CompactlyGenerated.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 72 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CompleteLatticestatement and proof · cited by 1,048
- List.TFAE.outproof · cited by 177
- WellFoundedGTstatement and proof · cited by 114
- IsCompactElementproof · cited by 34
- CompleteLattice.IsSupFiniteCompactstatement and proof · cited by 10
- CompleteLattice.IsSupClosedCompactproof · cited by 9
- CompleteLattice.wellFoundedGT_characterisationsproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- TopologicalSpace.noetherianSpace_iff_opensproof · cited by 3
- CompleteLattice.IsSupFiniteCompact.wellFoundedGTproof · cited by 0
- CompleteLattice.isCompactlyGenerated_of_wellFoundedGTproof · cited by 0