          (HP (λ j : J, pr1 (E' ⦃ t1 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t1 j, t ⦄)))
          (E (h t1) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t1 j, t ⦄))%set,
           CoproductArrow J C (h t1) (λ i : J, h0 i))) t0))


Going to execute:
intro

TcDebug (0) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  ============================
   (∏ t0 : J → C,
    isofhlevel 1
      ((λ t1 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t1 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t1 j, t ⦄)))
          (E (h t1) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t1 j, t ⦄))%set,
           CoproductArrow J C (h t1) (λ i : J, h0 i))) t0))


Going to execute:
<coq-core.plugins.ltac::intro@0>

TcDebug (0) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
use impred; intro

TcDebug (0) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
use impred

TcDebug (0) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
simple_rapply p

TcDebug (0) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
fun p =>
  simple refine p ||
    simple refine (p _) ||
      simple refine (p _ _) ||
...                              simple refine (p _ _ _ _ _ _ _ _ _ _ _ _ _ _)
                               || simple refine
                               (p _ _ _ _ _ _ _ _ _ _ _ _ _ _ _)

TcDebug (1) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
simple refine p ||
  simple refine (p _) ||
    simple refine (p _ _) ||
      simple refine (p _ _ _) ||
        simple refine (p _ _ _ _) ||
          simple refine (p _ _ _ _ _) ||
            simple refine (p _ _ _ _ _ _) ||
              simple refine (p _ _ _ _ _ _ _) ||
                simple refine (p _ _ _ _ _ _ _ _) ||
                  simple refine (p _ _ _ _ _ _ _ _ _) ||
                    simple refine (p _ _ _ _ _ _ _ _ _ _) ||
                      simple refine (p _ _ _ _ _ _ _ _ _ _ _) ||
                        simple refine (p _ _ _ _ _ _ _ _ _ _ _ _) ||
                          simple refine (p _ _ _ _ _ _ _ _ _ _ _ _ _) ||
                            simple refine (p _ _ _ _ _ _ _ _ _ _ _ _ _ _) ||
                              simple refine (p _ _ _ _ _ _ _ _ _ _ _ _ _ _ _)

TcDebug (1) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
simple refine p
Level 1: evaluation returns
simple refine p ||
  simple refine (p _) ||
    simple refine (p _ _) ||
      simple refine (p _ _ _) ||
        simple refine (p _ _ _ _) ||
          simple refine (p _ _ _ _ _) ||
            simple refine (p _ _ _ _ _ _) ||
              simple refine (p _ _ _ _ _ _ _) ||
                simple refine (p _ _ _ _ _ _ _ _) ||
                  simple refine (p _ _ _ _ _ _ _ _ _) ||
                    simple refine (p _ _ _ _ _ _ _ _ _ _) ||
                      simple refine (p _ _ _ _ _ _ _ _ _ _ _) ||
                        simple refine (p _ _ _ _ _ _ _ _ _ _ _ _) ||
                          simple refine (p _ _ _ _ _ _ _ _ _ _ _ _ _) ||
                            simple refine (p _ _ _ _ _ _ _ _ _ _ _ _ _ _) ||
                              simple refine (p _ _ _ _ _ _ _ _ _ _ _ _ _ _ _)
where
p := impred
of type
uconstr of type tacvalue


TcDebug (0) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
<coq-core.plugins.ltac::simple_refine@0> $1

TcDebug (0) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
simple refine (p _) ||
  simple refine (p _ _) ||
    simple refine (p _ _ _) ||
      simple refine (p _ _ _ _) ||
        simple refine (p _ _ _ _ _) ||
          simple refine (p _ _ _ _ _ _) ||
            simple refine (p _ _ _ _ _ _ _) ||
              simple refine (p _ _ _ _ _ _ _ _) ||
                simple refine (p _ _ _ _ _ _ _ _ _) ||
                  simple refine (p _ _ _ _ _ _ _ _ _ _) ||
                    simple refine (p _ _ _ _ _ _ _ _ _ _ _) ||
                      simple refine (p _ _ _ _ _ _ _ _ _ _ _ _) ||
                        simple refine (p _ _ _ _ _ _ _ _ _ _ _ _ _) ||
                          simple refine (p _ _ _ _ _ _ _ _ _ _ _ _ _ _) ||
                            simple refine (p _ _ _ _ _ _ _ _ _ _ _ _ _ _ _)
Level 0: In environment
P : hset_cartesian_closed_struct
C : category
E : struct_enrichment P C
E' := make_enrichment_over_struct P C E
 : enrichment C (sym_mon_closed_cat_of_hset_struct P)
J : UU
HP : hset_struct_type_prod P J
HC : is_univalent C
h : (∏ a : J → C, Coproduct J C a),,
    impred 1 (Coproduct J C) (λ t : J → C, isaprop_Coproduct HC J t)
t : C
t0 : J → C
The term "impred" has type
 "∏ (n : nat) (T : UU) (P : T → UU),
  (∏ t : T, isofhlevel n (P t)) → isofhlevel n (∏ t : T, P t)"
while it is expected to have type
 "isofhlevel 1
    (mor_hset_struct P
       (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
       (E (h t0) t)
       (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
        CoproductArrow J C (h t0) (λ i : J, h0 i)))"
(cannot unify "mor_hset_struct P
                 (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄))
                    (λ j : J, pr2 (E' ⦃ t0 j, t ⦄))) 
                 (E (h t0) t)
                 (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
                  CoproductArrow J C (h t0) (λ i : J, h0 i))" and 
"nat").
Level 0: In environment
P : hset_cartesian_closed_struct
C : category
E : struct_enrichment P C
E' := make_enrichment_over_struct P C E
 : enrichment C (sym_mon_closed_cat_of_hset_struct P)
J : UU
HP : hset_struct_type_prod P J
HC : is_univalent C
h : (∏ a : J → C, Coproduct J C a),,
    impred 1 (Coproduct J C) (λ t : J → C, isaprop_Coproduct HC J t)
t : C
t0 : J → C
The term "impred" has type
 "∏ (n : nat) (T : UU) (P : T → UU),
  (∏ t : T, isofhlevel n (P t)) → isofhlevel n (∏ t : T, P t)"
while it is expected to have type
 "isofhlevel 1
    (mor_hset_struct P
       (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
       (E (h t0) t)
       (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
        CoproductArrow J C (h t0) (λ i : J, h0 i)))"
(cannot unify "mor_hset_struct P
                 (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄))
                    (λ j : J, pr2 (E' ⦃ t0 j, t ⦄))) 
                 (E (h t0) t)
                 (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
                  CoproductArrow J C (h t0) (λ i : J, h0 i))" and 
"nat").

TcDebug (0) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
simple refine (p _)

TcDebug (0) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
<coq-core.plugins.ltac::simple_refine@0> $1

TcDebug (0) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
simple refine (p _ _) ||
  simple refine (p _ _ _) ||
    simple refine (p _ _ _ _) ||
      simple refine (p _ _ _ _ _) ||
        simple refine (p _ _ _ _ _ _) ||
          simple refine (p _ _ _ _ _ _ _) ||
            simple refine (p _ _ _ _ _ _ _ _) ||
              simple refine (p _ _ _ _ _ _ _ _ _) ||
                simple refine (p _ _ _ _ _ _ _ _ _ _) ||
                  simple refine (p _ _ _ _ _ _ _ _ _ _ _) ||
                    simple refine (p _ _ _ _ _ _ _ _ _ _ _ _) ||
                      simple refine (p _ _ _ _ _ _ _ _ _ _ _ _ _) ||
                        simple refine (p _ _ _ _ _ _ _ _ _ _ _ _ _ _) ||
                          simple refine (p _ _ _ _ _ _ _ _ _ _ _ _ _ _ _)
Level 0: In environment
P : hset_cartesian_closed_struct
C : category
E : struct_enrichment P C
E' := make_enrichment_over_struct P C E
 : enrichment C (sym_mon_closed_cat_of_hset_struct P)
J : UU
HP : hset_struct_type_prod P J
HC : is_univalent C
h : (∏ a : J → C, Coproduct J C a),,
    impred 1 (Coproduct J C) (λ t : J → C, isaprop_Coproduct HC J t)
t : C
t0 : J → C
The term "@impred ?n" has type
 "∏ (T : UU) (P0 : T → UU),
  (∏ t1 : T, isofhlevel ?n (P0 t1)) → isofhlevel ?n (∏ t : T, P0 t)"
while it is expected to have type
 "isofhlevel 1
    (mor_hset_struct P
       (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
       (E (h t0) t)
       (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
        CoproductArrow J C (h t0) (λ i : J, h0 i)))"
(cannot unify "mor_hset_struct P
                 (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄))
                    (λ j : J, pr2 (E' ⦃ t0 j, t ⦄))) 
                 (E (h t0) t)
                 (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
                  CoproductArrow J C (h t0) (λ i : J, h0 i))" and 
"UU").
Level 0: In environment
P : hset_cartesian_closed_struct
C : category
E : struct_enrichment P C
E' := make_enrichment_over_struct P C E
 : enrichment C (sym_mon_closed_cat_of_hset_struct P)
J : UU
HP : hset_struct_type_prod P J
HC : is_univalent C
h : (∏ a : J → C, Coproduct J C a),,
    impred 1 (Coproduct J C) (λ t : J → C, isaprop_Coproduct HC J t)
t : C
t0 : J → C
The term "@impred ?n" has type
 "∏ (T : UU) (P0 : T → UU),
  (∏ t1 : T, isofhlevel ?n (P0 t1)) → isofhlevel ?n (∏ t : T, P0 t)"
while it is expected to have type
 "isofhlevel 1
    (mor_hset_struct P
       (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
       (E (h t0) t)
       (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
        CoproductArrow J C (h t0) (λ i : J, h0 i)))"
(cannot unify "mor_hset_struct P
                 (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄))
                    (λ j : J, pr2 (E' ⦃ t0 j, t ⦄))) 
                 (E (h t0) t)
                 (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
                  CoproductArrow J C (h t0) (λ i : J, h0 i))" and 
"UU").

TcDebug (0) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
simple refine (p _ _)

TcDebug (0) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
<coq-core.plugins.ltac::simple_refine@0> $1

TcDebug (0) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
simple refine (p _ _ _) ||
  simple refine (p _ _ _ _) ||
    simple refine (p _ _ _ _ _) ||
      simple refine (p _ _ _ _ _ _) ||
        simple refine (p _ _ _ _ _ _ _) ||
          simple refine (p _ _ _ _ _ _ _ _) ||
            simple refine (p _ _ _ _ _ _ _ _ _) ||
              simple refine (p _ _ _ _ _ _ _ _ _ _) ||
                simple refine (p _ _ _ _ _ _ _ _ _ _ _) ||
                  simple refine (p _ _ _ _ _ _ _ _ _ _ _ _) ||
                    simple refine (p _ _ _ _ _ _ _ _ _ _ _ _ _) ||
                      simple refine (p _ _ _ _ _ _ _ _ _ _ _ _ _ _) || simple
                       refine (p _ _ _ _ _ _ _ _ _ _ _ _ _ _ _)
Level 0: In environment
P : hset_cartesian_closed_struct
C : category
E : struct_enrichment P C
E' := make_enrichment_over_struct P C E
 : enrichment C (sym_mon_closed_cat_of_hset_struct P)
J : UU
HP : hset_struct_type_prod P J
HC : is_univalent C
h : (∏ a : J → C, Coproduct J C a),,
    impred 1 (Coproduct J C) (λ t : J → C, isaprop_Coproduct HC J t)
t : C
t0 : J → C
The term "impred ?n" has type
 "∏ P0 : ?T → UU,
  (∏ t1 : ?T, isofhlevel ?n (P0 t1)) → isofhlevel ?n (∏ t : ?T, P0 t)"
while it is expected to have type
 "isofhlevel 1
    (mor_hset_struct P
       (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
       (E (h t0) t)
       (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
        CoproductArrow J C (h t0) (λ i : J, h0 i)))".
Level 0: In environment
P : hset_cartesian_closed_struct
C : category
E : struct_enrichment P C
E' := make_enrichment_over_struct P C E
 : enrichment C (sym_mon_closed_cat_of_hset_struct P)
J : UU
HP : hset_struct_type_prod P J
HC : is_univalent C
h : (∏ a : J → C, Coproduct J C a),,
    impred 1 (Coproduct J C) (λ t : J → C, isaprop_Coproduct HC J t)
t : C
t0 : J → C
The term "impred ?n" has type
 "∏ P0 : ?T → UU,
  (∏ t1 : ?T, isofhlevel ?n (P0 t1)) → isofhlevel ?n (∏ t : ?T, P0 t)"
while it is expected to have type
 "isofhlevel 1
    (mor_hset_struct P
       (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
       (E (h t0) t)
       (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
        CoproductArrow J C (h t0) (λ i : J, h0 i)))".

TcDebug (0) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
simple refine (p _ _ _)

TcDebug (0) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
<coq-core.plugins.ltac::simple_refine@0> $1

TcDebug (0) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
simple refine (p _ _ _ _) ||
  simple refine (p _ _ _ _ _) ||
    simple refine (p _ _ _ _ _ _) ||
      simple refine (p _ _ _ _ _ _ _) ||
        simple refine (p _ _ _ _ _ _ _ _) ||
          simple refine (p _ _ _ _ _ _ _ _ _) ||
            simple refine (p _ _ _ _ _ _ _ _ _ _) ||
              simple refine (p _ _ _ _ _ _ _ _ _ _ _) ||
                simple refine (p _ _ _ _ _ _ _ _ _ _ _ _) ||
                  simple refine (p _ _ _ _ _ _ _ _ _ _ _ _ _) ||
                    simple refine (p _ _ _ _ _ _ _ _ _ _ _ _ _ _) || simple
                     refine (p _ _ _ _ _ _ _ _ _ _ _ _ _ _ _)
Level 0: In environment
P : hset_cartesian_closed_struct
C : category
E : struct_enrichment P C
E' := make_enrichment_over_struct P C E
 : enrichment C (sym_mon_closed_cat_of_hset_struct P)
J : UU
HP : hset_struct_type_prod P J
HC : is_univalent C
h : (∏ a : J → C, Coproduct J C a),,
    impred 1 (Coproduct J C) (λ t : J → C, isaprop_Coproduct HC J t)
t : C
t0 : J → C
The term "impred ?n ?P" has type
 "(∏ t1 : ?T, isofhlevel ?n (?P t1)) → isofhlevel ?n (∏ t1 : ?T, ?P t1)"
while it is expected to have type
 "isofhlevel 1
    (mor_hset_struct P
       (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
       (E (h t0) t)
       (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
        CoproductArrow J C (h t0) (λ i : J, h0 i)))".
Level 0: In environment
P : hset_cartesian_closed_struct
C : category
E : struct_enrichment P C
E' := make_enrichment_over_struct P C E
 : enrichment C (sym_mon_closed_cat_of_hset_struct P)
J : UU
HP : hset_struct_type_prod P J
HC : is_univalent C
h : (∏ a : J → C, Coproduct J C a),,
    impred 1 (Coproduct J C) (λ t : J → C, isaprop_Coproduct HC J t)
t : C
t0 : J → C
The term "impred ?n ?P" has type
 "(∏ t1 : ?T, isofhlevel ?n (?P t1)) → isofhlevel ?n (∏ t1 : ?T, ?P t1)"
while it is expected to have type
 "isofhlevel 1
    (mor_hset_struct P
       (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
       (E (h t0) t)
       (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
        CoproductArrow J C (h t0) (λ i : J, h0 i)))".

TcDebug (0) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
simple refine (p _ _ _ _)

TcDebug (0) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
<coq-core.plugins.ltac::simple_refine@0> $1

TcDebug (0) > 
Goal:
  
  P : hset_cartesian_closed_struct
  C : category
  E : struct_enrichment P C
  E' := make_enrichment_over_struct P C E
     : enrichment C (sym_mon_closed_cat_of_hset_struct P)
  J : UU
  HP : hset_struct_type_prod P J
  HC : is_univalent C
  h : hProptoType
        (?X240@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0},,
         ?X242@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=?M0})
  t : ?X479@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
             ?M0; __:=?M0; __:=?M0; __:=?M0}
  t0 : ?X511@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
              ?M0}
  ============================
   (isofhlevel 1
      ((λ t0 : J → C,
        mor_hset_struct P
          (HP (λ j : J, pr1 (E' ⦃ t0 j, t ⦄)) (λ j : J, pr2 (E' ⦃ t0 j, t ⦄)))
          (E (h t0) t)
          (λ h0 : (∏ j : J, pr1 (E' ⦃ t0 j, t ⦄))%set,
           CoproductArrow J C (h t0) (λ i : J, h0 i))) t0))


Going to execute:
simple refine (p _ _ _ _ _) ||
  simple refine (p _ _ _ _ _ _) ||
    simple refine (p _ _ _ _ _ _ _) ||
      simple refine (p _ _ _ _ _ _ _ _) ||
        simple refine (p _ _ _ _ _ _ _ _ _) ||
          simple refine (p _ _ _ _ _ _ _ _ _ _) ||
            simple refine (p _ _ _ _ _ _ _ _ _ _ _) ||
              simple refine (p _ _ _ _ _ _ _ _ _ _ _ _) ||
                simple refine (p _ _ _ _ _ _ _ _ _ _ _ _ _) ||
                  simple refine (p _ _ _ _ _ _ _ _ _ _ _ _ _ _) || simple
                   refine (p _ _ _ _ _ _ _ _ _ _ _ _ _ _ _)
Level 0: In environment
P : hset_cartesian_closed_struct
C : category
E : struct_enrichment P C
E' := make_enrichment_over_struct P C E
 : enrichment C (sym_mon_closed_cat_of_hset_struct P)
J : UU
HP : hset_struct_type_prod P J
HC : is_univalent C
