Theorems · Definition · order theory

LTSeries.map

{α : Type u_1} →
  {β : Type u_2} → [inst : Preorder α] → [inst_1 : Preorder β] → LTSeries α → (f : α → β) → StrictMono f → LTSeries β

For two preorders α, β, if f : α → β is strictly monotonic, then a strict chain of α can be pushed out to a strict chain of β by a₀ < a₁ < ... < aₙ ↦ f a₀ < f a₁ < ... < f aₙ

Defined in

Mathlib.Order.RelSeries

Cited by

15 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderPreorder