Theorems · Theorem · order theory
Finset.sup_univ_eq_iSup
∀ {α : Type u_2} {β : Type u_3} [inst : Fintype α] [inst_1 : CompleteLattice β] (f : α → β), Finset.univ.sup f = iSup fA special case of Finset.sup_eq_iSup that omits the useless x ∈ univ binder.
- Defined in
- Mathlib.Data.Fintype.Lattice
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeCompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Finset.univstatement and proof · cited by 3,473
- iSupstatement and proof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- Finset.supstatement · cited by 530
- Finset.mem_univproof · cited by 361
- iSup_posproof · cited by 61
- Finset.sup_eq_iSupproof · cited by 30
Cited by3
Results whose statement or proof uses this declaration.
- Finset.inf_univ_eq_iInfproof · cited by 1
- UniformOnFun.edist_eq_pi_restrictproof · cited by 0
- Fin.edist_append_eq_max_edistproof · cited by 0