Theorems · Theorem · order theory
Finset.apply_sup_eq_sup_comp_of_nonempty
∀ {α : Type u_2} {β : Type u_3} {ι : Type u_5} [inst : LinearOrder α] {s : Finset ι} {f : ι → α} [inst_1 : OrderBot α]
[inst_2 : SemilatticeSup β] [inst_3 : OrderBot β] {g : α → β}, Monotone g → s.Nonempty → g (s.sup f) = s.sup (g ∘ f)- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Monotonestatement and proof · cited by 1,397
- OrderBotstatement and proof · cited by 1,055
- Finset.Nonemptystatement and proof · cited by 1,001
- SemilatticeSupstatement and proof · cited by 785
- Finset.supstatement and proof · cited by 530
- Finset.sup'proof · cited by 174
- Finset.sup'_eq_supproof · cited by 35
- Finset.apply_sup'_eq_sup'_compproof · cited by 11
- Monotone.map_supproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- Finset.sum_eq_sum_range_sdiffproof · cited by 1
- MvPolynomial.degreeOf_mul_X_eq_degreeOf_add_one_iffproof · cited by 1
- Finset.comp_sup_eq_sup_comp_of_nonemptyproof · cited by 0
- Finset.prod_eq_prod_range_sdiffproof · cited by 0