Theorems · Theorem · order theory
isLUB_Iio
∀ {γ : Type u_3} [inst : LinearOrder γ] [DenselyOrdered γ] {a : γ}, IsLUB (Set.Iio a) a- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- LinearOrderDenselyOrdered
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.
- LinearOrderstatement and proof · cited by 8,572
- le_of_ltproof · cited by 1,175
- Set.Iiostatement and proof · cited by 1,166
- DenselyOrderedstatement and proof · cited by 471
- IsLUBstatement · cited by 280
- upperBoundsproof · cited by 263
- le_of_forall_lt_imp_le_of_denseproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- upperBounds_Iioproof · cited by 0