lean2/tests/lean/finset_induction_bug.lean.expected.out

finset_induction_bug.lean:30:23: error:invalid 'rewrite' tactic, step produced type incorrect term, details: type mismatch at application
  @subtype.tag (list A) (@nodup A) x nodup_al'
term
  nodup_al'
has type
  @nodup A (@cons A a l')
but is expected to have type
  @nodup A x
rewrite step failed using pattern
  @cons A_1 a_1 l'_1
proof state:
A : Type,
h : decidable_eq A,
P : finset A → Prop,
H1 : P (@empty A),
H2 : ∀ ⦃s : finset A⦄ {a : A}, not (@mem A a s) → P s → P (@insert A (λ (a b : A), h a b) a s),
s : finset A,
u : nodup_list A,
l : list A,
a : A,
l' : list A,
IH :
  ∀ (x : @nodup A l'),
    P (@quot.mk (nodup_list A) (nodup_list_setoid A) (@subtype.tag (list A) (λ (l : list A), @nodup A l) l' x)),
nodup_al' : @nodup A (@cons A a l'),
anl' : not (@list.mem A a l'),
H3 : @eq (list A) (@list.insert A (λ (a b : A), h a b) a l') (@cons A a l'),
nodup_l' : @nodup A l',
P_l' :
  P (@quot.mk (nodup_list A) (nodup_list_setoid A) (@subtype.tag (list A) (λ (l : list A), @nodup A l) l' nodup_l')),
H4 :
  P
    (@insert A (λ (a b : A), h a b) a
       (@quot.mk (nodup_list A) (nodup_list_setoid A)
          (@subtype.tag (list A) (λ (l : list A), @nodup A l) l' nodup_l')))
⊢ P
    (@quot.mk (nodup_list A) (nodup_list_setoid A)
       (@subtype.tag (list A) (λ (l : list A), @nodup A l) (@cons A a l') nodup_al'))
finset_induction_bug.lean:30:45: error: don't know how to synthesize placeholder
A : Type,
h : decidable_eq A,
P : finset A → Prop,
H1 : P (@empty A),
H2 : ∀ ⦃s : finset A⦄ {a : A}, not (@mem A a s) → P s → P (@insert A (λ (a b : A), h a b) a s),
s : finset A,
u : nodup_list A,
l : list A,
a : A,
l' : list A,
IH :
  ∀ (x : @nodup A l'),
    P (@quot.mk (nodup_list A) (nodup_list_setoid A) (@subtype.tag (list A) (λ (l : list A), @nodup A l) l' x)),
nodup_al' : @nodup A (@cons A a l'),
anl' : not (@list.mem A a l'),
H3 : @eq (list A) (@list.insert A (λ (a b : A), h a b) a l') (@cons A a l'),
nodup_l' : @nodup A l',
P_l' :
  P (@quot.mk (nodup_list A) (nodup_list_setoid A) (@subtype.tag (list A) (λ (l : list A), @nodup A l) l' nodup_l')),
H4 :
  P
    (@insert A (λ (a b : A), h a b) a
       (@quot.mk (nodup_list A) (nodup_list_setoid A)
          (@subtype.tag (list A) (λ (l : list A), @nodup A l) l' nodup_l')))
⊢ P
    (@quot.mk (nodup_list A) (nodup_list_setoid A)
       (@subtype.tag (list A) (λ (l : list A), @nodup A l) (@cons A a l') nodup_al'))
finset_induction_bug.lean:16:5: error: failed to add declaration 'finset.induction₂' to environment, value has metavariables
remark: set 'formatter.hide_full_terms' to false to see the complete term
  λ (A : Type) (h : …) (P : …) (H1 : …) (H2 : …) (s : …),
    @quot.induction_on … … … s
      (λ (u : …),
         @subtype.destruct … … … u
           (λ (l : …),
              @list.induction_on A … l …
                (λ (a : A) (l' : …) (IH : …) (nodup_al' : …),
                   assert anl' : …, from …,
                   assert H3 : …, from …,
                   assert nodup_l' : …, from …,
                   assert P_l' : …, from …,
                   assert H4 : …, from …,
                   ?M_1)))
finset_induction_bug.lean:30:49: error: invalid end of module, expecting 'end'