Theorems · Theorem · order theory

Set.Finite.map_sSup_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 (sSup s) = sSup (f '' s)

Defined in: Mathlib.Order.ConditionallyCompleteLattice.Finset
Cited by: 0 results in Mathlib
Foundations: Depth 75 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
SupSet.sSupstatement · cited by 954
ConditionallyCompleteLinearOrderstatement and proof · cited by 542
ConditionallyCompleteLatticestatement and proof · cited by 364
Set.Finite.bddAboveproof · cited by 19
Set.Nonempty.csSup_memproof · cited by 11
Monotone.le_csSup_imageproof · cited by 2

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