Theorems · Theorem · order theory
Finset.isGLB_mem
∀ {α : Type u_2} [inst : LinearOrder α] {i : α} (s : Finset α), IsGLB (↑s) i → s.Nonempty → i ∈ s- Defined in
- Mathlib.Data.Finset.Max
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 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.
Cites7
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
- Finset.Nonemptystatement and proof · cited by 1,001
- IsGLBstatement and proof · cited by 213
- Finset.mem_coeproof · cited by 91
- Finset.isGLB_iff_isLeastproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Finset.isLUB_memproof · cited by 0
- LinearLocallyFiniteOrder.isMax_of_succFn_leproof · cited by 0