Theorems · Theorem · combinatorics
Finset.truncatedInf_of_mem
∀ {α : Type u_1} [inst : SemilatticeInf α] {s : Finset α} {a : α} [inst_1 : DecidableLE α] [inst_2 : BoundedOrder α]
(h : a ∈ upperClosure ↑s), s.truncatedInf a = {b ∈ s | b ≤ a}.inf' ⋯ id- Cited by
- 4 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Finset.filterstatement · cited by 949
- SemilatticeInfstatement and proof · cited by 634
- BoundedOrderstatement and proof · cited by 270
- UpperSetstatement · cited by 245
- Finset.inf'statement · cited by 117
- upperClosurestatement and proof · cited by 84
- Finset.truncatedInfstatement · cited by 19
Cited by4
Results whose statement or proof uses this declaration.
- Finset.truncatedInf_union_leftproof · cited by 2
- Finset.truncatedInf_supsproof · cited by 1
- Finset.truncatedInf_unionproof · cited by 1
- Finset.truncatedInf_of_isAntichainproof · cited by 1