Theorems · Theorem · order theory
csInf_Ioo
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {a b : α} [DenselyOrdered α], b < a → sInf (Set.Ioo b a) = b- Cited by
- 4 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.Ioostatement · cited by 1,214
- InfSet.sInfstatement · cited by 935
- DenselyOrderedstatement and proof · cited by 471
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Set.nonempty_Iooproof · cited by 23
- IsGLB.csInf_eqproof · cited by 13
- isGLB_Iooproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Real.ediam_Iooproof · cited by 3
- DirichletCharacter.absicssaOfAbsConv_eq_oneproof · cited by 2
- MeasureTheory.levyProkhorovEDist_selfproof · cited by 1
- ArithmeticFunction.abscissaOfAbsConv_moebiusproof · cited by 0