Theorems · Theorem · order theory

Monotone.csSup_image_le_map_csSup

∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLattice β] [inst_1 : ConditionallyCompleteLattice α]
  {f : α → β} {s : Set α},
  s.Nonempty →
    Monotone f → autoParam (BddAbove s) Monotone.csSup_image_le_map_csSup._auto_1 → sSup (f '' s) ≤ f (sSup s)

Defined in: Mathlib.Order.ConditionallyCompleteLattice.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 12 from the axioms · uses propext, Quot.sound
Assumes: ConditionallyCompleteLattice ConditionallyCompleteLattice

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement and proof · cited by 53,352
Set.imagestatement · cited by 5,609
Set.Nonemptystatement and proof · cited by 2,627
Monotonestatement and proof · cited by 1,397
SupSet.sSupstatement · cited by 954
BddAbovestatement and proof · cited by 620
ConditionallyCompleteLatticestatement and proof · cited by 364
isLUB_csSupproof · cited by 34
Monotone.csSup_image_leproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

Set.Finite.map_sSup_of_monotoneproof · cited by 0