Theorems · Theorem · order theory
sInf_le_sSup
∀ {α : Type u_1} [inst : CompleteLattice α] {s : Set α}, s.Nonempty → sInf s ≤ sSup s- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- CompleteLattice
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Cites8
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
- Set.Nonemptystatement and proof · cited by 2,627
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement · cited by 954
- InfSet.sInfstatement · cited by 935
- isGLB_sInfproof · cited by 23
- isLUB_sSupproof · cited by 21
- isGLB_le_isLUBproof · cited by 3
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