Theorems · Theorem · order theory

sInf_prod

∀ {α : Type u_1} {β : Type u_2} [inst : InfSet α] [inst_1 : InfSet β] {s : Set α} {t : Set β},
  s.Nonempty → t.Nonempty → sInf (s ×ˢ t) = (sInf s, sInf t)

Defined in: Mathlib.Order.CompleteLattice.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: InfSet InfSet

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Setstatement and proof · cited by 53,352
Set.Nonemptystatement and proof · cited by 2,627
SProd.sprodstatement · cited by 1,750
InfSet.sInfstatement and proof · cited by 935
InfSetstatement and proof · cited by 145
Set.fst_image_prodproof · cited by 8
Set.snd_image_prodproof · cited by 7

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