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Theorems · Theorem · order theory

iInf_prod

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : CompleteLattice α] {f : β × γ → α}, ⨅ x, f x = ⨅ i, ⨅ j, f (i, j)
Defined in
Mathlib.Order.CompleteLattice.Basic
Cited by
7 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext, Quot.sound
Assumes
CompleteLattice
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Filter.prod_atTop_atTop_eq · cited by 20Filter.prod_atTop_atTop_eqbiInf_prod · cited by 4biInf_prodiInf_unpair · cited by 3iInf_unpairiInf_sup_iInf · cited by 3iInf_sup_iInfiInf_prod' · cited by 2iInf_prod'Metric.infEDist_prod · cited by 2Metric.infEDist_prodFilter.prod_def · cited by 1Filter.prod_defiInf · cited by 1690iInfCompleteLattice · cited by 1048CompleteLatticeeq_of_forall_le_iff · cited by 65eq_of_forall_le_iffle_iInf_iff · cited by 30le_iInf_iffiInf_prodCITED BYCITES

Cites4

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Cited by7

Results whose statement or proof uses this declaration.