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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  ============================
   ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
     · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
    · precomp_arr E' z
        (enriched_coprod_cocone_in1 E' x y
           make_structure_enriched_binary_coprod_cocone) = f)


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)
EBC : structure_enrichment_binary_coprod
x, y, z : C
X : sym_mon_closed_cat_of_hset_struct P
f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
The term "@eq_mor_hset_struct ?P ?X" has type
 "∏ (Y : category_of_hset_struct ?P)
  (f0 g0 : category_of_hset_struct ?P ⟦ ?X, Y ⟧),
  (∏ x : pr11 ?X, pr1 f0 x = pr1 g0 x) → f0 = g0"
while it is expected to have type
 "(prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
  · structure_enrichment_binary_coprod_pair EBC x y z
  · precomp_arr E' z
      (enriched_coprod_cocone_in1 E' x y
         make_structure_enriched_binary_coprod_cocone) = f".
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)
EBC : structure_enrichment_binary_coprod
x, y, z : C
X : sym_mon_closed_cat_of_hset_struct P
f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
The term "@eq_mor_hset_struct ?P ?X" has type
 "∏ (Y : category_of_hset_struct ?P)
  (f0 g0 : category_of_hset_struct ?P ⟦ ?X, Y ⟧),
  (∏ x : pr11 ?X, pr1 f0 x = pr1 g0 x) → f0 = g0"
while it is expected to have type
 "(prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
  · structure_enrichment_binary_coprod_pair EBC x y z
  · precomp_arr E' z
      (enriched_coprod_cocone_in1 E' x y
         make_structure_enriched_binary_coprod_cocone) = f".

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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  ============================
   ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
     · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
    · precomp_arr E' z
        (enriched_coprod_cocone_in1 E' x y
           make_structure_enriched_binary_coprod_cocone) = f)


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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  ============================
   ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
     · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
    · precomp_arr E' z
        (enriched_coprod_cocone_in1 E' x y
           make_structure_enriched_binary_coprod_cocone) = f)


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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  ============================
   ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
     · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
    · precomp_arr E' z
        (enriched_coprod_cocone_in1 E' x y
           make_structure_enriched_binary_coprod_cocone) = f)


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)
EBC : structure_enrichment_binary_coprod
x, y, z : C
X : sym_mon_closed_cat_of_hset_struct P
f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
The term "@eq_mor_hset_struct ?P ?X ?Y" has type
 "∏ f0 g0 : category_of_hset_struct ?P ⟦ ?X, ?Y ⟧,
  (∏ x0 : pr11 ?X, pr1 f0 x0 = pr1 g0 x0) → f0 = g0"
while it is expected to have type
 "(prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
  · structure_enrichment_binary_coprod_pair EBC x y z
  · precomp_arr E' z
      (enriched_coprod_cocone_in1 E' x y
         make_structure_enriched_binary_coprod_cocone) = f".
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)
EBC : structure_enrichment_binary_coprod
x, y, z : C
X : sym_mon_closed_cat_of_hset_struct P
f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
The term "@eq_mor_hset_struct ?P ?X ?Y" has type
 "∏ f0 g0 : category_of_hset_struct ?P ⟦ ?X, ?Y ⟧,
  (∏ x0 : pr11 ?X, pr1 f0 x0 = pr1 g0 x0) → f0 = g0"
while it is expected to have type
 "(prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
  · structure_enrichment_binary_coprod_pair EBC x y z
  · precomp_arr E' z
      (enriched_coprod_cocone_in1 E' x y
         make_structure_enriched_binary_coprod_cocone) = f".

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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  ============================
   ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
     · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
    · precomp_arr E' z
        (enriched_coprod_cocone_in1 E' x y
           make_structure_enriched_binary_coprod_cocone) = f)


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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  ============================
   ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
     · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
    · precomp_arr E' z
        (enriched_coprod_cocone_in1 E' x y
           make_structure_enriched_binary_coprod_cocone) = f)


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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  ============================
   ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
     · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
    · precomp_arr E' z
        (enriched_coprod_cocone_in1 E' x y
           make_structure_enriched_binary_coprod_cocone) = f)


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)
EBC : structure_enrichment_binary_coprod
x, y, z : C
X : sym_mon_closed_cat_of_hset_struct P
f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
The term "@eq_mor_hset_struct ?P ?X ?Y ?f" has type
 "∏ g0 : category_of_hset_struct ?P ⟦ ?X, ?Y ⟧,
  (∏ x0 : pr11 ?X, pr1 ?f x0 = pr1 g0 x0) → ?f = g0"
while it is expected to have type
 "(prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
  · structure_enrichment_binary_coprod_pair EBC x y z
  · precomp_arr E' z
      (enriched_coprod_cocone_in1 E' x y
         make_structure_enriched_binary_coprod_cocone) = f".
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)
EBC : structure_enrichment_binary_coprod
x, y, z : C
X : sym_mon_closed_cat_of_hset_struct P
f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
The term "@eq_mor_hset_struct ?P ?X ?Y ?f" has type
 "∏ g0 : category_of_hset_struct ?P ⟦ ?X, ?Y ⟧,
  (∏ x0 : pr11 ?X, pr1 ?f x0 = pr1 g0 x0) → ?f = g0"
while it is expected to have type
 "(prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
  · structure_enrichment_binary_coprod_pair EBC x y z
  · precomp_arr E' z
      (enriched_coprod_cocone_in1 E' x y
         make_structure_enriched_binary_coprod_cocone) = f".

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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  ============================
   ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
     · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
    · precomp_arr E' z
        (enriched_coprod_cocone_in1 E' x y
           make_structure_enriched_binary_coprod_cocone) = f)


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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  ============================
   ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
     · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
    · precomp_arr E' z
        (enriched_coprod_cocone_in1 E' x y
           make_structure_enriched_binary_coprod_cocone) = f)


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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  ============================
   ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
     · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
    · precomp_arr E' z
        (enriched_coprod_cocone_in1 E' x y
           make_structure_enriched_binary_coprod_cocone) = f)


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 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _)
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)
EBC : structure_enrichment_binary_coprod
x, y, z : C
X : sym_mon_closed_cat_of_hset_struct P
f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
The term "eq_mor_hset_struct ?P" has type
 "(∏ x0 : pr11 ?X, pr1 ?f x0 = pr1 ?g x0) → ?f = ?g"
while it is expected to have type
 "(prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
  · structure_enrichment_binary_coprod_pair EBC x y z
  · precomp_arr E' z
      (enriched_coprod_cocone_in1 E' x y
         make_structure_enriched_binary_coprod_cocone) = f".
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)
EBC : structure_enrichment_binary_coprod
x, y, z : C
X : sym_mon_closed_cat_of_hset_struct P
f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
The term "eq_mor_hset_struct ?P" has type
 "(∏ x0 : pr11 ?X, pr1 ?f x0 = pr1 ?g x0) → ?f = ?g"
while it is expected to have type
 "(prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
  · structure_enrichment_binary_coprod_pair EBC x y z
  · precomp_arr E' z
      (enriched_coprod_cocone_in1 E' x y
         make_structure_enriched_binary_coprod_cocone) = f".

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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  ============================
   ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
     · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
    · precomp_arr E' z
        (enriched_coprod_cocone_in1 E' x y
           make_structure_enriched_binary_coprod_cocone) = f)


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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  ============================
   ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
     · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
    · precomp_arr E' z
        (enriched_coprod_cocone_in1 E' x y
           make_structure_enriched_binary_coprod_cocone) = f)


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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  ============================
   (∏ x0 : pr11 X,
    pr1
      ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
        (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
        (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
        (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
        · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
       · precomp_arr E' z
           (enriched_coprod_cocone_in1 E' x y
              make_structure_enriched_binary_coprod_cocone)) x0 = 
    pr1 f x0)


Going to execute:
intros w

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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  w : pr11 ?X384@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0}
  ============================
   (pr1
      ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
        (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
        (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
        (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
        · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
       · precomp_arr E' z
           (enriched_coprod_cocone_in1 E' x y
              make_structure_enriched_binary_coprod_cocone)) w = 
    pr1 f w)


Going to execute:
cbn

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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  w : pr11 ?X384@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0}
  ============================
   (structure_enrichment_obj_in1 EBC x y
    · BinCoproductArrow (pr1 EBC x y) (pr1 f w) (pr1 g w) = 
    pr1 f w)


Going to execute:
apply structure_enrichment_obj_in1_sum

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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  ============================
   (∏ (w : C) (v : sym_mon_closed_cat_of_hset_struct P)
    (f : sym_mon_closed_cat_of_hset_struct P ⟦ v, E' ⦃ x, w ⦄ ⟧)
    (g : sym_mon_closed_cat_of_hset_struct P ⟦ v, E' ⦃ y, w ⦄ ⟧),
    (λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f0 : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g0 : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f0,, pr1 g0),,
      hset_struct_pair P (pr2 f0) (pr2 g0))
     · structure_enrichment_binary_coprod_pair EBC x y z) w v f g
    · precomp_arr E' w
        (enriched_coprod_cocone_in2 E' x y
           make_structure_enriched_binary_coprod_cocone) = g)


Going to execute:
intros z X f g; use eq_mor_hset_struct; intros w; cbn;
 apply structure_enrichment_obj_in2_sum
Evaluated term: structure_enrichment_obj_in1_sum

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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  ============================
   (∏ (w : C) (v : sym_mon_closed_cat_of_hset_struct P)
    (f : sym_mon_closed_cat_of_hset_struct P ⟦ v, E' ⦃ x, w ⦄ ⟧)
    (g : sym_mon_closed_cat_of_hset_struct P ⟦ v, E' ⦃ y, w ⦄ ⟧),
    (λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f0 : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g0 : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f0,, pr1 g0),,
      hset_struct_pair P (pr2 f0) (pr2 g0))
     · structure_enrichment_binary_coprod_pair EBC x y z) w v f g
    · precomp_arr E' w
        (enriched_coprod_cocone_in2 E' x y
           make_structure_enriched_binary_coprod_cocone) = g)


Going to execute:
intros z X f g; use eq_mor_hset_struct; intros w; cbn

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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  ============================
   (∏ (w : C) (v : sym_mon_closed_cat_of_hset_struct P)
    (f : sym_mon_closed_cat_of_hset_struct P ⟦ v, E' ⦃ x, w ⦄ ⟧)
    (g : sym_mon_closed_cat_of_hset_struct P ⟦ v, E' ⦃ y, w ⦄ ⟧),
    (λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f0 : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g0 : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f0,, pr1 g0),,
      hset_struct_pair P (pr2 f0) (pr2 g0))
     · structure_enrichment_binary_coprod_pair EBC x y z) w v f g
    · precomp_arr E' w
        (enriched_coprod_cocone_in2 E' x y
           make_structure_enriched_binary_coprod_cocone) = g)


Going to execute:
intros z X f g; use eq_mor_hset_struct; intros w

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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  ============================
   (∏ (w : C) (v : sym_mon_closed_cat_of_hset_struct P)
    (f : sym_mon_closed_cat_of_hset_struct P ⟦ v, E' ⦃ x, w ⦄ ⟧)
    (g : sym_mon_closed_cat_of_hset_struct P ⟦ v, E' ⦃ y, w ⦄ ⟧),
    (λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f0 : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g0 : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f0,, pr1 g0),,
      hset_struct_pair P (pr2 f0) (pr2 g0))
     · structure_enrichment_binary_coprod_pair EBC x y z) w v f g
    · precomp_arr E' w
        (enriched_coprod_cocone_in2 E' x y
           make_structure_enriched_binary_coprod_cocone) = g)


Going to execute:
intros z X f g; use eq_mor_hset_struct

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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  ============================
   (∏ (w : C) (v : sym_mon_closed_cat_of_hset_struct P)
    (f : sym_mon_closed_cat_of_hset_struct P ⟦ v, E' ⦃ x, w ⦄ ⟧)
    (g : sym_mon_closed_cat_of_hset_struct P ⟦ v, E' ⦃ y, w ⦄ ⟧),
    (λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f0 : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g0 : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f0,, pr1 g0),,
      hset_struct_pair P (pr2 f0) (pr2 g0))
     · structure_enrichment_binary_coprod_pair EBC x y z) w v f g
    · precomp_arr E' w
        (enriched_coprod_cocone_in2 E' x y
           make_structure_enriched_binary_coprod_cocone) = g)


Going to execute:
intros z X f g

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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  ============================
   ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
     · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
    · precomp_arr E' z
        (enriched_coprod_cocone_in2 E' x y
           make_structure_enriched_binary_coprod_cocone) = g)


Going to execute:
use eq_mor_hset_struct

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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  ============================
   ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
     · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
    · precomp_arr E' z
        (enriched_coprod_cocone_in2 E' x y
           make_structure_enriched_binary_coprod_cocone) = g)


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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  ============================
   ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
     · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
    · precomp_arr E' z
        (enriched_coprod_cocone_in2 E' x y
           make_structure_enriched_binary_coprod_cocone) = g)


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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  ============================
   ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
     · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
    · precomp_arr E' z
        (enriched_coprod_cocone_in2 E' x y
           make_structure_enriched_binary_coprod_cocone) = g)


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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  ============================
   ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
     · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
    · precomp_arr E' z
        (enriched_coprod_cocone_in2 E' x y
           make_structure_enriched_binary_coprod_cocone) = g)


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 := eq_mor_hset_struct
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)
  EBC : structure_enrichment_binary_coprod
  x : ob C
  y : ob C
  z : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧
  g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧
  ============================
   ((λ (z : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (f : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ x, z ⦄ ⟧)
     (g : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, z ⦄ ⟧),
     (prodtofuntoprod (pr1 f,, pr1 g),, hset_struct_pair P (pr2 f) (pr2 g))
     · structure_enrichment_binary_coprod_pair EBC x y z) z X f g
    · precomp_arr E' z
        (enriched_coprod_cocone_in2 E' x y
