Theorems · Theorem · order theory

Order.IsNormal.ext_iff

∀ {α : Type u_1} {β : Type u_2} {f : α → β} [inst : LinearOrder α] [WellFoundedLT α] [inst_2 : SuccOrder α]
  [inst_3 : LinearOrder β] [inst_4 : OrderBot α] {g : α → β},
  Order.IsNormal f → Order.IsNormal g → (f = g ↔ f ⊥ = g ⊥ ∧ ∀ (a : α), f a = g a → f (Order.succ a) = g (Order.succ a))

Defined in

Mathlib.Order.IsNormal

Cited by

4 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderWellFoundedLTSuccOrderLinearOrderOrderBot