Theorems · Theorem · order theory
isGLB_lt_iff
∀ {α : Type u_1} [inst : LinearOrder α] {s : Set α} {a b : α}, IsGLB s a → (a < b ↔ ∃ c ∈ s, c < b)- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 6 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.
Cites6
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
- not_leproof · cited by 328
- IsGLBstatement and proof · cited by 213
- mem_lowerBoundsproof · cited by 19
- le_isGLB_iffproof · cited by 17
Cited by6
Results whose statement or proof uses this declaration.
- sInf_lt_iffproof · cited by 7
- IsGLB.exists_betweenproof · cited by 5
- csInf_lt_iffproof · cited by 4
- IsPreconnected.Ioi_csInf_subsetproof · cited by 2
- exists_countable_upperSemicontinuous_isGLBproof · cited by 1
- IsConnected.Ioo_csInf_csSup_subsetproof · cited by 1