Theorems · Theorem · order theory
Finset.sup_mono
∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeSup α] [inst_1 : OrderBot α] {s₁ s₂ : Finset β} {f : β → α},
s₁ ⊆ s₂ → s₁.sup f ≤ s₂.sup f- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 56 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.
Cites6
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.le_supproof · cited by 112
- Finset.sup_leproof · cited by 44
Cited by25
Results whose statement or proof uses this declaration.
- Finset.supIndep_iff_disjoint_eraseproof · cited by 6
- AddMonoidAlgebra.sup_support_coeff_add_leproof · cited by 5
- AddMonoidAlgebra.sup_support_coeff_mul_leproof · cited by 5
- AddMonoidAlgebra.supDegree_sum_leproof · cited by 3
- MonomialOrder.degree_monomial_leproof · cited by 3
- Finset.sup_erase_botproof · cited by 2
- Finset.shadow_monotoneproof · cited by 2
- CompleteLattice.WellFoundedGT.isSupFiniteCompactproof · cited by 2
- MvPolynomial.degrees_map_leproof · cited by 2
- MvPowerSeries.totalDegree_truncFinsetproof · cited by 2
- Polynomial.degree_erase_leproof · cited by 2
- Finset.max_monoproof · cited by 1