  X : ob (sym_mon_closed_cat_of_hset_struct P)
  φ₁ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  q : φ₁
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone) =
      φ₂
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone)
  ============================
   (φ₁ = φ₂)


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)
  φ₁ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  q : φ₁
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone) =
      φ₂
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone)
  ============================
   (φ₁ = φ₂)


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)
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
φ₁,
φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
     E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
q : φ₁
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) =
    φ₂
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone)
The term "eq_mor_hset_struct" has type
 "∏ (P : hset_struct) (X Y : category_of_hset_struct P)
  (f g : category_of_hset_struct P ⟦ X, Y ⟧),
  (∏ x : pr11 X, pr1 f x = pr1 g x) → f = g"
while it is expected to have type "φ₁ = φ₂".
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
φ₁,
φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
     E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
q : φ₁
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) =
    φ₂
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone)
The term "eq_mor_hset_struct" has type
 "∏ (P : hset_struct) (X Y : category_of_hset_struct P)
  (f g : category_of_hset_struct P ⟦ X, Y ⟧),
  (∏ x : pr11 X, pr1 f x = pr1 g x) → f = g"
while it is expected to have type "φ₁ = φ₂".

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)
  φ₁ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  q : φ₁
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone) =
      φ₂
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone)
  ============================
   (φ₁ = φ₂)


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)
  φ₁ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  q : φ₁
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone) =
      φ₂
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone)
  ============================
   (φ₁ = φ₂)


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)
  φ₁ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  q : φ₁
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone) =
      φ₂
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone)
  ============================
   (φ₁ = φ₂)


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
φ₁,
φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
     E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
q : φ₁
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) =
    φ₂
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone)
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 "φ₁ = φ₂".
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
φ₁,
φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
     E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
q : φ₁
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) =
    φ₂
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone)
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 "φ₁ = φ₂".

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)
  φ₁ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  q : φ₁
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone) =
      φ₂
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone)
  ============================
   (φ₁ = φ₂)


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)
  φ₁ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  q : φ₁
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone) =
      φ₂
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone)
  ============================
   (φ₁ = φ₂)


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)
  φ₁ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  q : φ₁
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone) =
      φ₂
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone)
  ============================
   (φ₁ = φ₂)


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
φ₁,
φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
     E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
q : φ₁
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) =
    φ₂
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone)
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 "φ₁ = φ₂".
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
φ₁,
φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
     E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
q : φ₁
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) =
    φ₂
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone)
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 "φ₁ = φ₂".

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)
  φ₁ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  q : φ₁
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone) =
      φ₂
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone)
  ============================
   (φ₁ = φ₂)


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)
  φ₁ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  q : φ₁
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone) =
      φ₂
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone)
  ============================
   (φ₁ = φ₂)


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)
  φ₁ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  q : φ₁
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone) =
      φ₂
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone)
  ============================
   (φ₁ = φ₂)


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
φ₁,
φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
     E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
q : φ₁
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) =
    φ₂
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone)
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 "φ₁ = φ₂".
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
φ₁,
φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
     E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
q : φ₁
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) =
    φ₂
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone)
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 "φ₁ = φ₂".

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)
  φ₁ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  q : φ₁
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone) =
      φ₂
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone)
  ============================
   (φ₁ = φ₂)


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)
  φ₁ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  q : φ₁
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone) =
      φ₂
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone)
  ============================
   (φ₁ = φ₂)


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)
  φ₁ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  q : φ₁
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone) =
      φ₂
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone)
  ============================
   (φ₁ = φ₂)


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
φ₁,
φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
     E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
q : φ₁
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) =
    φ₂
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone)
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 "φ₁ = φ₂".
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
φ₁,
φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
     E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
q : φ₁
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) =
    φ₂
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone)
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 "φ₁ = φ₂".

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)
  φ₁ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  q : φ₁
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone) =
      φ₂
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone)
  ============================
   (φ₁ = φ₂)


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)
  φ₁ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  q : φ₁
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone) =
      φ₂
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone)
  ============================
   (φ₁ = φ₂)


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)
  φ₁ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  q : φ₁
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone) =
      φ₂
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
             make_structure_enrichment_coequalizer_cocone)
  ============================
   (φ₁ = φ₂)


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
φ₁,
φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
     E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
q : φ₁
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) =
    φ₂
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone)
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 "φ₁ = φ₂".
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
φ₁,
φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
     E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
q : φ₁
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone) =
    φ₂
    · precomp_arr E' w
        (enriched_coequalizer_cocone_in E' f g
           make_structure_enrichment_coequalizer_cocone)
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 "φ₁ = φ₂".

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)
  φ₁ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  φ₂ : sym_mon_closed_cat_of_hset_struct P ⟦ X,
       E' ⦃ make_structure_enrichment_coequalizer_cocone, w ⦄ ⟧
  q : φ₁
      · precomp_arr E' w
          (enriched_coequalizer_cocone_in E' f g
