Theorems · Theorem · order theory
WellFoundedGT.finite_of_sSupIndep
∀ {α : Type u_2} [inst : CompleteLattice α] [WellFoundedGT α] {s : Set α}, sSupIndep s → s.Finite- Defined in
- Mathlib.Order.CompactlyGenerated.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLatticeWellFoundedGT
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- Bot.botproof · cited by 4,720
- Disjointproof · cited by 2,201
- Set.Finitestatement and proof · cited by 1,814
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupproof · cited by 954
- Finset.supproof · cited by 530
- Set.Infiniteproof · cited by 263
- Finset.finite_toSetproof · cited by 210
- Finset.coe_insertproof · cited by 124
Cited by2
Results whose statement or proof uses this declaration.
- WellFoundedGT.finite_ne_bot_of_iSupIndepproof · cited by 5
- IsSemisimpleModule.finite_tfaeproof · cited by 2