Theorems · Theorem · combinatorics
Set.infs_self_subset
∀ {α : Type u_2} [inst : SemilatticeInf α] {s : Set α}, s ⊼ s ⊆ s ↔ InfClosed s- Defined in
- Mathlib.Data.Set.Sups
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeInf
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- SemilatticeInfstatement and proof · cited by 634
- HasInfs.infsstatement · cited by 105
- InfClosedstatement · cited by 57
- Set.hasInfsstatement · cited by 43
- Set.infs_subset_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Set.infs_selfproof · cited by 0