  
  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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  w : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
  q : h · precomp_arr E' w f = h · precomp_arr E' w g
  ============================
   ((λ (w : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧)
     (q : h · precomp_arr E' w f = h · precomp_arr E' w g),
     ((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
      make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
     · structure_enrichment_to_coequalizer EEC f g) w X h q
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) = h)


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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  w : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
  q : h · precomp_arr E' w f = h · precomp_arr E' w g
  ============================
   ((λ (w : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧)
     (q : h · precomp_arr E' w f = h · precomp_arr E' w g),
     ((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
      make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
     · structure_enrichment_to_coequalizer EEC f g) w X h q
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) = h)


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)
HP : hset_equalizer_struct P
EEC : structure_enrichment_coequalizers
x, y : C
f, g : C ⟦ x, y ⟧
w : C
X : sym_mon_closed_cat_of_hset_struct P
h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
q : h · precomp_arr E' w f = h · precomp_arr E' w g
The term "@eq_mor_hset_struct ?P" has type
 "∏ (X0 Y : category_of_hset_struct ?P)
  (f0 g0 : category_of_hset_struct ?P ⟦ X0, Y ⟧),
  (∏ x : pr11 X0, pr1 f0 x = pr1 g0 x) → f0 = g0"
while it is expected to have type
 "((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
   make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
  · structure_enrichment_to_coequalizer EEC f g
  · precomp_arr E' w
      (enriched_coequalizer_cocone_in E' f g
         make_structure_enrichment_coequalizer_cocone) = h".
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)
HP : hset_equalizer_struct P
EEC : structure_enrichment_coequalizers
x, y : C
f, g : C ⟦ x, y ⟧
w : C
X : sym_mon_closed_cat_of_hset_struct P
h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
q : h · precomp_arr E' w f = h · precomp_arr E' w g
The term "@eq_mor_hset_struct ?P" has type
 "∏ (X0 Y : category_of_hset_struct ?P)
  (f0 g0 : category_of_hset_struct ?P ⟦ X0, Y ⟧),
  (∏ x : pr11 X0, pr1 f0 x = pr1 g0 x) → f0 = g0"
while it is expected to have type
 "((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
   make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
  · structure_enrichment_to_coequalizer EEC f g
  · precomp_arr E' w
      (enriched_coequalizer_cocone_in E' f g
         make_structure_enrichment_coequalizer_cocone) = h".

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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  w : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
  q : h · precomp_arr E' w f = h · precomp_arr E' w g
  ============================
   ((λ (w : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧)
     (q : h · precomp_arr E' w f = h · precomp_arr E' w g),
     ((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
      make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
     · structure_enrichment_to_coequalizer EEC f g) w X h q
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) = h)


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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  w : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
  q : h · precomp_arr E' w f = h · precomp_arr E' w g
  ============================
   ((λ (w : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧)
     (q : h · precomp_arr E' w f = h · precomp_arr E' w g),
     ((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
      make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
     · structure_enrichment_to_coequalizer EEC f g) w X h q
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) = h)


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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  w : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
  q : h · precomp_arr E' w f = h · precomp_arr E' w g
  ============================
   ((λ (w : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧)
     (q : h · precomp_arr E' w f = h · precomp_arr E' w g),
     ((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
      make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
     · structure_enrichment_to_coequalizer EEC f g) w X h q
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) = h)


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)
HP : hset_equalizer_struct P
EEC : structure_enrichment_coequalizers
x, y : C
f, g : C ⟦ x, y ⟧
w : C
X : sym_mon_closed_cat_of_hset_struct P
h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
q : h · precomp_arr E' w f = h · precomp_arr E' w g
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
 "((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
   make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
  · structure_enrichment_to_coequalizer EEC f g
  · precomp_arr E' w
      (enriched_coequalizer_cocone_in E' f g
         make_structure_enrichment_coequalizer_cocone) = h".
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)
HP : hset_equalizer_struct P
EEC : structure_enrichment_coequalizers
x, y : C
f, g : C ⟦ x, y ⟧
w : C
X : sym_mon_closed_cat_of_hset_struct P
h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
q : h · precomp_arr E' w f = h · precomp_arr E' w g
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
 "((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
   make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
  · structure_enrichment_to_coequalizer EEC f g
  · precomp_arr E' w
      (enriched_coequalizer_cocone_in E' f g
         make_structure_enrichment_coequalizer_cocone) = h".

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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  w : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
  q : h · precomp_arr E' w f = h · precomp_arr E' w g
  ============================
   ((λ (w : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧)
     (q : h · precomp_arr E' w f = h · precomp_arr E' w g),
     ((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
      make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
     · structure_enrichment_to_coequalizer EEC f g) w X h q
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) = h)


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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  w : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
  q : h · precomp_arr E' w f = h · precomp_arr E' w g
  ============================
   ((λ (w : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧)
     (q : h · precomp_arr E' w f = h · precomp_arr E' w g),
     ((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
      make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
     · structure_enrichment_to_coequalizer EEC f g) w X h q
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) = h)


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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  w : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
  q : h · precomp_arr E' w f = h · precomp_arr E' w g
  ============================
   ((λ (w : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧)
     (q : h · precomp_arr E' w f = h · precomp_arr E' w g),
     ((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
      make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
     · structure_enrichment_to_coequalizer EEC f g) w X h q
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) = h)


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)
HP : hset_equalizer_struct P
EEC : structure_enrichment_coequalizers
x, y : C
f, g : C ⟦ x, y ⟧
w : C
X : sym_mon_closed_cat_of_hset_struct P
h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
q : h · precomp_arr E' w f = h · precomp_arr E' w g
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
 "((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
   make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
  · structure_enrichment_to_coequalizer EEC f g
  · precomp_arr E' w
      (enriched_coequalizer_cocone_in E' f g
         make_structure_enrichment_coequalizer_cocone) = h".
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)
HP : hset_equalizer_struct P
EEC : structure_enrichment_coequalizers
x, y : C
f, g : C ⟦ x, y ⟧
w : C
X : sym_mon_closed_cat_of_hset_struct P
h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
q : h · precomp_arr E' w f = h · precomp_arr E' w g
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
 "((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
   make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
  · structure_enrichment_to_coequalizer EEC f g
  · precomp_arr E' w
      (enriched_coequalizer_cocone_in E' f g
         make_structure_enrichment_coequalizer_cocone) = h".

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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  w : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
  q : h · precomp_arr E' w f = h · precomp_arr E' w g
  ============================
   ((λ (w : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧)
     (q : h · precomp_arr E' w f = h · precomp_arr E' w g),
     ((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
      make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
     · structure_enrichment_to_coequalizer EEC f g) w X h q
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) = h)


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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  w : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
  q : h · precomp_arr E' w f = h · precomp_arr E' w g
  ============================
   ((λ (w : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧)
     (q : h · precomp_arr E' w f = h · precomp_arr E' w g),
     ((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
      make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
     · structure_enrichment_to_coequalizer EEC f g) w X h q
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) = h)


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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  w : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
  q : h · precomp_arr E' w f = h · precomp_arr E' w g
  ============================
   ((λ (w : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧)
     (q : h · precomp_arr E' w f = h · precomp_arr E' w g),
     ((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
      make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
     · structure_enrichment_to_coequalizer EEC f g) w X h q
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) = h)


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)
HP : hset_equalizer_struct P
EEC : structure_enrichment_coequalizers
x, y : C
f, g : C ⟦ x, y ⟧
w : C
X : sym_mon_closed_cat_of_hset_struct P
h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
q : h · precomp_arr E' w f = h · precomp_arr E' w g
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
 "((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
   make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
  · structure_enrichment_to_coequalizer EEC f g
  · precomp_arr E' w
      (enriched_coequalizer_cocone_in E' f g
         make_structure_enrichment_coequalizer_cocone) = h".
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)
HP : hset_equalizer_struct P
EEC : structure_enrichment_coequalizers
x, y : C
f, g : C ⟦ x, y ⟧
w : C
X : sym_mon_closed_cat_of_hset_struct P
h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
q : h · precomp_arr E' w f = h · precomp_arr E' w g
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
 "((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
   make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
  · structure_enrichment_to_coequalizer EEC f g
  · precomp_arr E' w
      (enriched_coequalizer_cocone_in E' f g
         make_structure_enrichment_coequalizer_cocone) = h".

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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  w : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
  q : h · precomp_arr E' w f = h · precomp_arr E' w g
  ============================
   ((λ (w : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧)
     (q : h · precomp_arr E' w f = h · precomp_arr E' w g),
     ((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
      make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
     · structure_enrichment_to_coequalizer EEC f g) w X h q
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) = h)


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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  w : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
  q : h · precomp_arr E' w f = h · precomp_arr E' w g
  ============================
   ((λ (w : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧)
     (q : h · precomp_arr E' w f = h · precomp_arr E' w g),
     ((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
      make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
     · structure_enrichment_to_coequalizer EEC f g) w X h q
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) = h)


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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  w : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
  q : h · precomp_arr E' w f = h · precomp_arr E' w g
  ============================
   ((λ (w : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧)
     (q : h · precomp_arr E' w f = h · precomp_arr E' w g),
     ((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
      make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
     · structure_enrichment_to_coequalizer EEC f g) w X h q
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) = h)


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)
HP : hset_equalizer_struct P
EEC : structure_enrichment_coequalizers
x, y : C
f, g : C ⟦ x, y ⟧
w : C
X : sym_mon_closed_cat_of_hset_struct P
h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
q : h · precomp_arr E' w f = h · precomp_arr E' w g
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
 "((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
   make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
  · structure_enrichment_to_coequalizer EEC f g
  · precomp_arr E' w
      (enriched_coequalizer_cocone_in E' f g
         make_structure_enrichment_coequalizer_cocone) = h".
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)
HP : hset_equalizer_struct P
EEC : structure_enrichment_coequalizers
x, y : C
f, g : C ⟦ x, y ⟧
w : C
X : sym_mon_closed_cat_of_hset_struct P
h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
q : h · precomp_arr E' w f = h · precomp_arr E' w g
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
 "((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
   make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
  · structure_enrichment_to_coequalizer EEC f g
  · precomp_arr E' w
      (enriched_coequalizer_cocone_in E' f g
         make_structure_enrichment_coequalizer_cocone) = h".

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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  w : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
  q : h · precomp_arr E' w f = h · precomp_arr E' w g
  ============================
   ((λ (w : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧)
     (q : h · precomp_arr E' w f = h · precomp_arr E' w g),
     ((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
      make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
     · structure_enrichment_to_coequalizer EEC f g) w X h q
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) = h)


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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  w : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
  q : h · precomp_arr E' w f = h · precomp_arr E' w g
  ============================
   ((λ (w : C) (X : sym_mon_closed_cat_of_hset_struct P)
     (h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧)
     (q : h · precomp_arr E' w f = h · precomp_arr E' w g),
     ((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
      make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h q)
     · structure_enrichment_to_coequalizer EEC f g) w X h q
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) = h)


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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  w : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
  q : h · precomp_arr E' w f = h · precomp_arr E' w g
  ============================
   (∏ x0 : pr11 X,
    pr1
      ((λ (w : C) (X : sym_mon_closed_cat_of_hset_struct P)
        (h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧)
        (q : h · precomp_arr E' w f = h · precomp_arr E' w g),
        ((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
         make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h
           q) · structure_enrichment_to_coequalizer EEC f g) w X h q
       · precomp_arr E' w
           (enriched_coequalizer_cocone_in E' f g
              make_structure_enrichment_coequalizer_cocone)) x0 = 
    pr1 h x0)


Going to execute:
intros z

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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  w : ob C
  X : ob (sym_mon_closed_cat_of_hset_struct P)
  h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧
  q : h · precomp_arr E' w f = h · precomp_arr E' w g
  z : pr11 ?X622@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0}
  ============================
   (pr1
      ((λ (w : C) (X : sym_mon_closed_cat_of_hset_struct P)
        (h : sym_mon_closed_cat_of_hset_struct P ⟦ X, E' ⦃ y, w ⦄ ⟧)
        (q : h · precomp_arr E' w f = h · precomp_arr E' w g),
        ((λ z : pr1 X, pr1 h z,, eqtohomot (maponpaths pr1 q) z),,
         make_structure_enrichment_coequalizer_is_coequalizer_subproof0 w X h
           q) · structure_enrichment_to_coequalizer EEC f g) w X h q
       · precomp_arr E' w
           (enriched_coequalizer_cocone_in E' f g
              make_structure_enrichment_coequalizer_cocone)) z = 
    pr1 h z)


Going to execute:
apply structure_enrichment_obj_from_coequalizer_in

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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  ============================
   (∑ a : enriched_coequalizer_cocone E' f g,
    is_coequalizer_enriched E' f g a)


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

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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  ============================
   (enriched_coequalizer_cocone E' f g)


Going to execute:
<coq-core.plugins.ltac::exact@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)
  HP : hset_equalizer_struct P
  EEC : structure_enrichment_coequalizers
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  ============================
   ((λ a : enriched_coequalizer_cocone E' f g,
     is_coequalizer_enriched E' f g a)
      (make_structure_enrichment_coequalizer_cocone EEC f g))


Going to execute:
<coq-core.plugins.ltac::exact@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)
  HP : hset_equalizer_struct P
  EEC : enrichment_coequalizers E'
  w : ob C
  x : ob C
  y : ob C
  f : C ⟦ x, y ⟧
  g : C ⟦ x, y ⟧
  Eq := Equalizers_category_of_hset_struct HP (E' ⦃ y, w ⦄) 
          (E' ⦃ x, w ⦄) (precomp_arr E' w f) (precomp_arr E' w g)
     : Equalizer (precomp_arr E' w f) (precomp_arr E' w g)
  Eq_pr := EqualizerArrow Eq : category_of_hset_struct P ⟦ Eq, E' ⦃ y, w ⦄ ⟧
  Eq_path := EqualizerEqAr Eq
          : Eq_pr · precomp_arr E' w f = Eq_pr · precomp_arr E' w g
  h : C ⟦ y, w ⟧
  q : f · h = g · h
  p := eqtohomot
         (maponpaths pr1
            (EqualizerCommutes
               (is_coequalizer_enriched_to_Equalizer E' f g
                  (pr2 (EEC x y f g)) w)
               ((∑ x0 : C ⟦ y, w ⟧, hProp_to_hSet (f · x0 = g · x0)%logic)%set,,
                hset_struct_equalizer HP
                  (Core.comp_disp
                     (Core.comp_disp
                        (hset_struct_pair P (Core.id_disp (E y w))
                           (hset_struct_to_unit P (E y w)))
                        (Core.comp_disp
