Theorems · Theorem · order theory
Finset.inf_prodMap
∀ {ι : Type u_7} {κ : Type u_8} {α : Type u_9} {β : Type u_10} [inst : SemilatticeInf α] [inst_1 : SemilatticeInf β]
[inst_2 : OrderTop α] [inst_3 : OrderTop β] {s : Finset ι} {t : Finset κ},
s.Nonempty → t.Nonempty → ∀ (f : ι → α) (g : κ → β), (s ×ˢ t).inf (Prod.map f g) = (s.inf f, t.inf g)- Defined in
- Mathlib.Data.Finset.Lattice.Prod
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites10
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
- SProd.sprodstatement · cited by 1,750
- Finset.Nonemptystatement and proof · cited by 1,001
- SemilatticeInfstatement and proof · cited by 634
- OrderTopstatement and proof · cited by 493
- Finset.infstatement · cited by 219
- eq_of_forall_le_iffproof · cited by 65
- Finset.mem_productproof · cited by 48
- Finset.le_inf_iffproof · cited by 12
- Prod.le_defproof · cited by 9
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