Theorems · Theorem · order theory
isGLB_Ioc
∀ {γ : Type u_3} [inst : SemilatticeSup γ] [DenselyOrdered γ] {a b : γ}, a < b → IsGLB (Set.Ioc a b) 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
- SemilatticeSupDenselyOrdered
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.Iocstatement · cited by 971
- SemilatticeSupstatement and proof · cited by 785
- DenselyOrderedstatement and proof · cited by 471
- IsGLBstatement · cited by 213
- Set.Ioc_subset_Icc_selfproof · cited by 53
- Set.Ioo_subset_Ioc_selfproof · cited by 30
- isGLB_Iooproof · cited by 5
- isGLB_Iccproof · cited by 2
- IsGLB.of_subset_of_supersetproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- lowerBounds_Iocproof · cited by 0
- left_nhdsWithin_Ioc_neBotproof · cited by 0
- csInf_Iocproof · cited by 0