Theorems · Theorem · order theory

MonotoneOn.sInf_image_Icc

∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : ConditionallyCompleteLattice β] {f : α → β} {a b : α},
  a ≤ b → MonotoneOn f (Set.Icc a b) → sInf (f '' Set.Icc a b) = f a

Defined in

Mathlib.Order.ConditionallyCompleteLattice.Basic

Cited by

1 results in Mathlib

Foundations

Depth 11 from the axioms · uses propext, Quot.sound

Assumes

PreorderConditionallyCompleteLattice