--#include "alfa/Test0.alfa"

open Logic  use  cong

open Module_Prelude  use  List,  id,  map

open Module_Test0  use  Id1,  MapId1,  IF

proofId1 ::Id1
  =  \(t21::Star) ->  \(x::t21) -> Ref@_

proofMapId1 ::MapId1
  =  \(a::Star) ->
     \(xs::Module_Prelude.List a) ->
    case xs of {
      (Nil) -> Ref@_;
      (Cons x xs') ->
        cong
        (List a)
        (List a)
        (map a a (id a) xs')
        xs'
        ( \(h::PreludeFromAlfa.List a) -> Cons@_ x h)
        (proofMapId1 a xs');}

proofIF ::IF
  =  \(t83::Star) ->
    AndIntro ((f::t83 -> t83) ->
              (g::t83 -> t83) ->
              (===) (t83 -> t83) (Module_Prelude.id (t83 -> t83) (Module_Prelude.(..)
                                                                  t83
                                                                  t83
                                                                  t83
                                                                  f
                                                                  g)) (Module_Prelude.(..)
                                                                       t83
                                                                       t83
                                                                       t83
                                                                       (Module_Prelude.id (t83 ->
                                                                                           t83) f)
                                                                       (Module_Prelude.id (t83 ->
                                                                                           t83) g))) ((===) (t83 ->
                                                                                                             t83) (Module_Prelude.id (t83 ->
                                                                                                                                      t83) (Module_Prelude.id
                                                                                                                                            t83)) (Module_Prelude.id
                                                                                                                                                   t83)) ( \(f::t83 ->
                                                                                                                                                                t83) ->
                                                                                                                                                           \(g::t83 ->
                                                                                                                                                                t83) ->
                                                                                                                                                          Ref@_) Ref@_
{-# Alfa unfoldgoals off
brief on
hidetypeannots on
wide

nd
hiding on
 #-}