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Theorems · Theorem · order theory

sSup_image2

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : CompleteLattice α] {f : β → γ → α} {s : Set β} {t : Set γ},
  sSup (Set.image2 f s t) = ⨆ a ∈ s, ⨆ b ∈ t, f a b
Defined in
Mathlib.Order.CompleteLattice.Basic
Cited by
3 results in Mathlib
Foundations
Depth 16 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.

sSup_symmDiff_sSup_le · cited by 1sSup_symmDiff_sSup_leMetric.ediam_eq_sSup · cited by 1Metric.ediam_eq_sSupSet.sUnion_image2 · cited by 0Set.sUnion_image2Set · cited by 53352SetiSup · cited by 2415iSupCompleteLattice · cited by 1048CompleteLatticeSupSet.sSup · cited by 954SupSet.sSupSet.image2 · cited by 311Set.image2sSup_image · cited by 36sSup_imageSet.image_prod · cited by 24Set.image_prodbiSup_prod · cited by 5biSup_prodsSup_image2CITED BYCITES

Cites8

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Cited by3

Results whose statement or proof uses this declaration.