             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)
  ============================
   (∏ x0 : pr11 X, pr1 φ₁ x0 = pr1 φ₂ x0)


Going to execute:
intro 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)
  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)
  ============================
   (∏ x0 : pr11 X, pr1 φ₁ x0 = pr1 φ₂ x0)


Going to execute:
<coq-core.plugins.ltac::intro@1> $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)
  z : pr11 ?X426@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0}
  ============================
   (pr1 φ₁ z = pr1 φ₂ z)


Going to execute:
use structure_enrichment_coequalizer_arr_eq

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)
  z : pr11 ?X426@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0}
  ============================
   (pr1 φ₁ z = pr1 φ₂ z)


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)
  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)
  z : pr11 ?X426@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0}
  ============================
   (pr1 φ₁ z = pr1 φ₂ z)


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)
  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)
  z : pr11 ?X426@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0}
  ============================
   (pr1 φ₁ z = pr1 φ₂ z)


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)
  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)
  z : pr11 ?X426@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0}
  ============================
   (pr1 φ₁ z = pr1 φ₂ z)


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 := structure_enrichment_coequalizer_arr_eq
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)
  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)
  z : pr11 ?X426@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0}
  ============================
   (pr1 φ₁ z = pr1 φ₂ z)


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)
  z : pr11 ?X426@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0}
  ============================
   (pr1 φ₁ z = pr1 φ₂ z)


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)
z : pr11 X
The term "structure_enrichment_coequalizer_arr_eq" has type
 "∏ (EEC : structure_enrichment_coequalizers) (w x y : C) 
  (f g : C ⟦ x, y ⟧)
  (h₁ h₂ : C ⟦ structure_enrichment_obj_coequalizer EEC f g, w ⟧),
  structure_enrichment_obj_coequalizer_in EEC f g · h₁ =
  structure_enrichment_obj_coequalizer_in EEC f g · h₂ → 
  h₁ = h₂" while it is expected to have type "pr1 φ₁ z = pr1 φ₂ z".
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)
z : pr11 X
The term "structure_enrichment_coequalizer_arr_eq" has type
 "∏ (EEC : structure_enrichment_coequalizers) (w x y : C) 
  (f g : C ⟦ x, y ⟧)
  (h₁ h₂ : C ⟦ structure_enrichment_obj_coequalizer EEC f g, w ⟧),
  structure_enrichment_obj_coequalizer_in EEC f g · h₁ =
  structure_enrichment_obj_coequalizer_in EEC f g · h₂ → 
  h₁ = h₂" while it is expected to have type "pr1 φ₁ z = pr1 φ₂ 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)
  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)
  z : pr11 ?X426@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0}
  ============================
   (pr1 φ₁ z = pr1 φ₂ z)


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)
  z : pr11 ?X426@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0}
  ============================
   (pr1 φ₁ z = pr1 φ₂ z)


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)
  z : pr11 ?X426@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0}
  ============================
   (pr1 φ₁ z = pr1 φ₂ z)


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)
z : pr11 X
The term "@structure_enrichment_coequalizer_arr_eq ?EEC" has type
 "∏ (w0 x0 y0 : C) (f0 g0 : C ⟦ x0, y0 ⟧)
  (h₁ h₂ : C ⟦ structure_enrichment_obj_coequalizer ?EEC f0 g0, w0 ⟧),
  structure_enrichment_obj_coequalizer_in ?EEC f0 g0 · h₁ =
  structure_enrichment_obj_coequalizer_in ?EEC f0 g0 · h₂ → 
  h₁ = h₂" while it is expected to have type "pr1 φ₁ z = pr1 φ₂ z".
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)
z : pr11 X
The term "@structure_enrichment_coequalizer_arr_eq ?EEC" has type
 "∏ (w0 x0 y0 : C) (f0 g0 : C ⟦ x0, y0 ⟧)
  (h₁ h₂ : C ⟦ structure_enrichment_obj_coequalizer ?EEC f0 g0, w0 ⟧),
  structure_enrichment_obj_coequalizer_in ?EEC f0 g0 · h₁ =
  structure_enrichment_obj_coequalizer_in ?EEC f0 g0 · h₂ → 
  h₁ = h₂" while it is expected to have type "pr1 φ₁ z = pr1 φ₂ 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)
  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)
  z : pr11 ?X426@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0}
  ============================
   (pr1 φ₁ z = pr1 φ₂ z)


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)
  z : pr11 ?X426@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0}
  ============================
   (pr1 φ₁ z = pr1 φ₂ z)


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)
  z : pr11 ?X426@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0}
  ============================
   (pr1 φ₁ z = pr1 φ₂ z)


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)
z : pr11 X
The term "@structure_enrichment_coequalizer_arr_eq ?EEC ?w" has type
 "∏ (x0 y0 : C) (f0 g0 : C ⟦ x0, y0 ⟧)
  (h₁ h₂ : C ⟦ structure_enrichment_obj_coequalizer ?EEC f0 g0, ?w ⟧),
  structure_enrichment_obj_coequalizer_in ?EEC f0 g0 · h₁ =
  structure_enrichment_obj_coequalizer_in ?EEC f0 g0 · h₂ → 
  h₁ = h₂" while it is expected to have type "pr1 φ₁ z = pr1 φ₂ z".
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)
z : pr11 X
The term "@structure_enrichment_coequalizer_arr_eq ?EEC ?w" has type
 "∏ (x0 y0 : C) (f0 g0 : C ⟦ x0, y0 ⟧)
  (h₁ h₂ : C ⟦ structure_enrichment_obj_coequalizer ?EEC f0 g0, ?w ⟧),
  structure_enrichment_obj_coequalizer_in ?EEC f0 g0 · h₁ =
  structure_enrichment_obj_coequalizer_in ?EEC f0 g0 · h₂ → 
  h₁ = h₂" while it is expected to have type "pr1 φ₁ z = pr1 φ₂ 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)
  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)
  z : pr11 ?X426@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0}
  ============================
   (pr1 φ₁ z = pr1 φ₂ z)


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)
  z : pr11 ?X426@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0}
  ============================
   (pr1 φ₁ z = pr1 φ₂ z)


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)
  z : pr11 ?X426@{__:=?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0; __:=?M0; __:=
                  ?M0; __:=?M0; __:=?M0}
  ============================
   (pr1 φ₁ z = pr1 φ₂ z)
