Theorems · Theorem · order theory
WellFoundedLT.finite_of_sSupIndep
∀ {α : Type u_2} [inst : CompleteLattice α] [WellFoundedLT α] {s : Set α}, sSupIndep s → s.Finite- Defined in
- Mathlib.Order.CompactlyGenerated.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLatticeWellFoundedLT
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Set.Elemproof · cited by 7,166
- Bot.botproof · cited by 4,720
- LE.le.transproof · cited by 3,151
- iSupproof · cited by 2,415
- Set.Finitestatement and proof · cited by 1,814
- le_rflproof · cited by 1,558
- CompleteLatticestatement and proof · cited by 1,048
- Function.Embeddingproof · cited by 988
- LT.lt.trans_leproof · cited by 678
- WellFoundedLTstatement and proof · cited by 491
Cited by2
Results whose statement or proof uses this declaration.
- IsSemisimpleModule.finite_tfaeproof · cited by 2
- WellFoundedLT.finite_ne_bot_of_iSupIndepproof · cited by 0