Theorems · Theorem · order theory

Set.Finite.map_sInf_of_monotone

∀ {α : Type u_2} {β : Type u_3} [inst : ConditionallyCompleteLinearOrder α] [inst_1 : ConditionallyCompleteLattice β]
  {f : α → β}, Monotone f → ∀ {s : Set α}, s.Nonempty → s.Finite → f (sInf s) = sInf (f '' s)

Defined in: Mathlib.Order.ConditionallyCompleteLattice.Finset
Cited by: 0 results in Mathlib
Foundations: Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: ConditionallyCompleteLinearOrder ConditionallyCompleteLattice

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Setstatement and proof · cited by 53,352
Set.imagestatement · cited by 5,609
Set.Nonemptystatement and proof · cited by 2,627
le_antisymmproof · cited by 2,068
Set.Finitestatement and proof · cited by 1,814
Monotonestatement and proof · cited by 1,397
InfSet.sInfstatement · cited by 935
ConditionallyCompleteLinearOrderstatement and proof · cited by 542
ConditionallyCompleteLatticestatement and proof · cited by 364
Set.Finite.bddBelowproof · cited by 7
Set.Nonempty.csInf_memproof · cited by 3
Monotone.csInf_image_leproof · cited by 2

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