Theorems · Theorem · order theory
lt_isLUB_iff
∀ {α : Type u_1} [inst : LinearOrder α] {s : Set α} {a b : α}, IsLUB s a → (b < a ↔ ∃ c ∈ s, b < c)- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- IsLUBstatement and proof · cited by 280
- isLUB_le_iffproof · cited by 24
Cited by7
Results whose statement or proof uses this declaration.
- IsLUB.exists_betweenproof · cited by 8
- Order.IsNormal.lt_iff_exists_ltproof · cited by 4
- lt_csSup_iffproof · cited by 4
- Measurable.isLUBproof · cited by 3
- lt_sSup_iffproof · cited by 2
- Sion.minimaxproof · cited by 2
- IsConnected.Ioo_csInf_csSup_subsetproof · cited by 1