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order.​order_iso_nat

order.​order_iso_nat

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rel_embedding.​nat_gt
rel_embedding.​nat_lt
rel_embedding.​well_founded_iff_no_descending_seq
source
def rel_embedding.​nat_lt {α : Type u_1} {r : α → α → Prop} [is_strict_order α r] (f : ℕ → α) :
(∀ (n : ℕ), r (f n) (f (n + 1))) → has_lt.lt ↪r r

Equations
source
def rel_embedding.​nat_gt {α : Type u_1} {r : α → α → Prop} [is_strict_order α r] (f : ℕ → α) :
(∀ (n : ℕ), r (f (n + 1)) (f n)) → gt ↪r r

Equations
source
theorem rel_embedding.​well_founded_iff_no_descending_seq {α : Type u_1} {r : α → α → Prop} [is_strict_order α r] :
well_founded r ↔ ¬nonempty (gt ↪r r)

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