Theorems · Theorem · order theory
csInf_Ioi
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {a : α} [NoMaxOrder α] [DenselyOrdered α], sInf (Set.Ioi a) = a- Cited by
- 3 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Set.Ioistatement · cited by 1,463
- le_of_ltproof · cited by 1,175
- InfSet.sInfstatement · cited by 935
- DenselyOrderedstatement and proof · cited by 471
- ConditionallyCompleteLatticestatement and proof · cited by 364
- NoMaxOrderstatement and proof · cited by 340
- Set.mem_Ioiproof · cited by 80
- Set.nonempty_Ioiproof · cited by 10
- exists_between'proof · cited by 8
- csInf_eq_of_forall_ge_of_forall_gt_exists_ltproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- gauge_zeroproof · cited by 7
- gauge_closure_zeroproof · cited by 1
- gauge_zero'proof · cited by 1