@[irreducible, specialize #[]]

def Std.Iter.inductSteps {α β : Type u_1} [Iterator α Id β] [Iterators.Finite α Id] (motive : Iter β → Sort x) (step : (it : Iter β) → ({it' : Iter β} → {out : β} → it.IsPlausibleStep (IterStep.yield it' out) → motive it') → ({it' : Iter β} → it.IsPlausibleStep (IterStep.skip it') → motive it') → motive it) (it : Iter β) : motive it

Induction principle for finite iterators: One can define a function f that maps every iterator it to an element of motive it by defining f it in terms of the values of f on the plausible successors of `it'.

Equations

• One or more equations did not get rendered due to their size.

@[irreducible, specialize #[]]

def Std.Iter.inductSkips {α β : Type u_1} [Iterator α Id β] [Iterators.Productive α Id] (motive : Iter β → Sort x) (step : (it : Iter β) → ({it' : Iter β} → it.IsPlausibleStep (IterStep.skip it') → motive it') → motive it) (it : Iter β) : motive it

Induction principle for productive iterators: One can define a function f that maps every iterator it to an element of motive it by defining f it in terms of the values of f on the plausible skip successors of `it'.

Equations

• Std.Iter.inductSkips motive step it = step it fun {it' : Std.Iter β} (x : it.IsPlausibleStep (Std.IterStep.skip it')) => Std.Iter.inductSkips motive step it'