Research proof index

our own variant of map_congr, for mapM -/ public theorem mapM_congr [Monad m] [LawfulMonad m] {f g : α → m β} : ∀ {l : List α}, (∀ x ∈ l, f x = g x) → mapM f l = mapM g l := by intro l rw [← mapM'_eq_mapM, ← mapM'_eq_mapM] exact mapM'_congr public theorem to_option_distr_mapM' {α β ε} {l : List α} {f: α → Except ε β} : (List.mapM' f l).toOption = (List.ma...

our own variant of map_congr, for mapM -/ public theorem mapM_congr [Monad m] [LawfulMonad m] {f g : α → m β} : ∀ {l : List α}, (∀ x ∈ l, f x = g x) → mapM f l = mapM g l := by intro l rw [← mapM'_eq_mapM, ← mapM'_eq_mapM] exact mapM'_congr public theorem to_option_distr_mapM' {α β ε} {l : List α} {f: α → Except ε β} : (List.mapM' f l).toOption = (List.ma...

Applying mapM on the RHS list of Forall₂ leads to new Forall₂ relation if certain conditions are met.

Note the converse is not true: counterexample R is =, xs is [1], ys is [1, 2]

kind of a transitivity property, if you squint

our own variant of map_congr, for filterMap -/ public theorem filterMap_congr {f g : α → Option β} : ∀ {l : List α}, (∀ x ∈ l, f x = g x) → filterMap f l = filterMap g l | [], _ => rfl | a :: l, h => by let ⟨h₁, h₂⟩ := forall_mem_cons.1 h rw [filterMap, filterMap, h₁, filterMap_congr h₂] public theorem filterMap_empty_iff_all_none {f : α → Option β} {xs :...