Theorems · Theorem · order theory
Finset.apply_inf_eq_inf_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 : OrderTop α]
[inst_2 : SemilatticeInf β] [inst_3 : OrderTop β] {g : α → β}, Monotone g → s.Nonempty → g (s.inf f) = s.inf (g ∘ f)- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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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
- Finset.Nonemptystatement and proof · cited by 1,001
- SemilatticeInfstatement and proof · cited by 634
- OrderTopstatement and proof · cited by 493
- Finset.infstatement and proof · cited by 219
- Finset.inf'proof · cited by 117
- Finset.inf'_eq_infproof · cited by 12
- Monotone.map_infproof · cited by 8
- Finset.apply_inf'_eq_inf'_compproof · cited by 6
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