Theorems · Theorem · order theory
sInf_upperBounds_eq_sSup
∀ {α : Type u_1} [inst : CompleteLattice α] (s : Set α), sInf (upperBounds s) = sSup s- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- CompleteLattice
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.
- Setstatement and proof · cited by 53,352
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement · cited by 954
- InfSet.sInfstatement · cited by 935
- upperBoundsstatement and proof · cited by 263
- IsLeast.isGLBproof · cited by 23
- isGLB_sInfproof · cited by 23
- isLUB_sSupproof · cited by 21
- IsGLB.uniqueproof · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- Filter.limsSup_principal_eq_sSupproof · cited by 1
- sInf_upperBounds_eq_csSupproof · cited by 0