Theorems · Theorem · order theory

Order.IsNormal.lt_iff_exists_lt

∀ {α : Type u_1} {β : Type u_2} {a : α} {f : α → β} [inst : LinearOrder α] [inst_1 : LinearOrder β],
  Order.IsNormal f → Order.IsSuccLimit a → ∀ {b : β}, b < f a ↔ ∃ a' < a, b < f a'

Defined in

Mathlib.Order.IsNormal

Cited by

4 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderLinearOrder