Theorems · Theorem · order theory
Finset.isGLB_iff_isLeast
∀ {α : Type u_2} [inst : LinearOrder α] (i : α) (s : Finset α), s.Nonempty → (IsGLB (↑s) i ↔ IsLeast (↑s) i)- Defined in
- Mathlib.Data.Finset.Max
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- LinearOrderstatement and proof · cited by 8,572
- SetLike.coestatement and proof · cited by 8,199
- le_antisymmproof · cited by 2,068
- Finset.Nonemptystatement and proof · cited by 1,001
- upperBoundsproof · cited by 263
- IsGLBstatement and proof · cited by 213
- lowerBoundsproof · cited by 212
- IsLeaststatement and proof · cited by 122
- Finset.min'proof · cited by 58
- Finset.min'_memproof · cited by 24
- IsLeast.isGLBproof · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- Finset.isGLB_memproof · cited by 2
- Finset.isLUB_iff_isGreatestproof · cited by 0