Theorems · Theorem · order theory
Interval.coe_sInf
∀ {α : Type u_1} [inst : CompleteLattice α] [inst_1 : DecidableLE α] (S : Set (Interval α)), ↑(sInf S) = ⋂ s ∈ S, ↑s- Defined in
- Mathlib.Order.Interval.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLatticeDecidableLE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- SetLike.coestatement and proof · cited by 8,199
- Bot.botproof · cited by 4,720
- LE.le.transproof · cited by 3,151
- Set.Nonemptyproof · cited by 2,627
- Set.extproof · cited by 2,266
- Set.iInterstatement and proof · cited by 1,084
- CompleteLatticestatement and proof · cited by 1,048
- InfSet.sInfstatement · cited by 935
- Set.Subset.rflproof · cited by 255
- NonemptyIntervalproof · cited by 139
- Intervalstatement and proof · cited by 76
Cited by1
Results whose statement or proof uses this declaration.
- Interval.coe_iInfproof · cited by 1