Theorems · Theorem · order theory
Finset.sup_congr
∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeSup α] [inst_1 : OrderBot α] {s₁ s₂ : Finset β} {f g : β → α},
s₁ = s₂ → (∀ a ∈ s₂, f a = g a) → s₁.sup f = s₂.sup g- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeSupOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- OrderBotstatement and proof · cited by 1,055
- SemilatticeSupstatement and proof · cited by 785
- Finset.supstatement · cited by 530
- Finset.fold_congrproof · cited by 11
Cited by9
Results whose statement or proof uses this declaration.
- partialSups_disjointedproof · cited by 5
- disjointed_eq_selfproof · cited by 1
- Finset.sup_preimage_selfproof · cited by 1
- BoxIntegral.TaggedPrepartition.distortion_of_constproof · cited by 1
- MvPolynomial.degrees_rename_of_injectiveproof · cited by 1
- Fintype.sup_disjointedproof · cited by 1
- BoxIntegral.Prepartition.distortion_of_constproof · cited by 0
- dist_inf_sup_piproof · cited by 0