Theorems · Theorem · order theory

monovaryOn_iff_exists_monotoneOn

∀ {ι : Type u_1} {α : Type u_3} {β : Type u_4} [inst : LinearOrder α] [inst_1 : LinearOrder β] {f : ι → α} {g : ι → β}
  {s : Set ι}, MonovaryOn f g s ↔ ∃ x, MonotoneOn f s ∧ MonotoneOn g s

Defined in

Mathlib.Order.Monotone.MonovaryOrder

Cited by

1 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderLinearOrder