Theorems · Theorem · order theory
isLUB_Ico
∀ {γ : Type u_3} [inst : SemilatticeInf γ] [DenselyOrdered γ] {a b : γ}, b < a → IsLUB (Set.Ico b a) a- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeInfDenselyOrdered
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LT.lt.leproof · cited by 2,189
- Set.Icostatement · cited by 799
- SemilatticeInfstatement and proof · cited by 634
- DenselyOrderedstatement and proof · cited by 471
- IsLUBstatement · cited by 280
- Set.Ico_subset_Icc_selfproof · cited by 41
- Set.Ioo_subset_Ico_selfproof · cited by 29
- isLUB_Iooproof · cited by 7
- isLUB_Iccproof · cited by 2
- IsLUB.of_subset_of_supersetproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- csSup_Icoproof · cited by 0
- upperBounds_Icoproof · cited by 0
- right_nhdsWithin_Ico_neBotproof · cited by 0