Goal:
  
  A : Type
  B : Type
  R : A → B → Type
  x : A
  y : list B
  a1' : list A
  a1 : list B
  a : All2 R a1' a1
  ============================
   ({| pr1 := [x]; pr2 := y |} = {| pr1 := a1'; pr2 := a1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in ∑ y' : B, y = [y'] × R x y')


DEBUG:Going to execute:
destruct p

Goals:
    A : Type  B : Type  R : A → B → Type  x : A  y : list B
  ============================
   ({| pr1 := [x]; pr2 := y |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in ∑ y' : B, y = [y'] × R x y')

  
  A : Type
  B : Type
  R : A → B → Type
  x : A
  y : list B
  x0 : A
  y0 : B
  l : list A
  l' : list B
  r : R x0 y0
  a : All2 R l l'
  ============================
   ({| pr1 := [x]; pr2 := y |} = {| pr1 := x0 :: l; pr2 := y0 :: l' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in ∑ y' : B, y = [y'] × R x y')


DEBUG:Going to execute:
DepElim.simpl_dep_elim

Goals:
    A : Type  B : Type  R : A → B → Type  x : A  y : list B
  ============================
   ({| pr1 := [x]; pr2 := y |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in ∑ y' : B, y = [y'] × R x y')

  
  A : Type
  B : Type
  R : A → B → Type
  x : A
  y : list B
  x0 : A
  y0 : B
  l : list A
  l' : list B
  r : R x0 y0
  a : All2 R l l'
  ============================
   ({| pr1 := [x]; pr2 := y |} = {| pr1 := x0 :: l; pr2 := y0 :: l' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in ∑ y' : B, y = [y'] × R x y')


DEBUG:Going to execute:
DepElim.simplify_dep_elim; DepElim.simplify_IH_hyps;
            DepElim.unblock_dep_elim

Goals:
    A : Type  B : Type  R : A → B → Type  x : A  y : list B
  ============================
   ({| pr1 := [x]; pr2 := y |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in ∑ y' : B, y = [y'] × R x y')

  
  A : Type
  B : Type
  R : A → B → Type
  x : A
  y : list B
  x0 : A
  y0 : B
  l : list A
  l' : list B
  r : R x0 y0
  a : All2 R l l'
  ============================
   ({| pr1 := [x]; pr2 := y |} = {| pr1 := x0 :: l; pr2 := y0 :: l' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in ∑ y' : B, y = [y'] × R x y')


DEBUG:Going to execute:
DepElim.simplify_dep_elim; DepElim.simplify_IH_hyps

Goals:
    A : Type  B : Type  R : A → B → Type  x : A  y : list B
  ============================
   ({| pr1 := [x]; pr2 := y |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in ∑ y' : B, y = [y'] × R x y')

  
  A : Type
  B : Type
  R : A → B → Type
  x : A
  y : list B
  x0 : A
  y0 : B
  l : list A
  l' : list B
  r : R x0 y0
  a : All2 R l l'
  ============================
   ({| pr1 := [x]; pr2 := y |} = {| pr1 := x0 :: l; pr2 := y0 :: l' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in ∑ y' : B, y = [y'] × R x y')


DEBUG:Going to execute:
DepElim.simplify_dep_elim

Goals:
    A : Type  B : Type  R : A → B → Type  x : A  y : list B
  ============================
   ({| pr1 := [x]; pr2 := y |} = {| pr1 := []; pr2 := [] |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in ∑ y' : B, y = [y'] × R x y')

  
  A : Type
  B : Type
  R : A → B → Type
  x : A
  y : list B
  x0 : A
  y0 : B
  l : list A
  l' : list B
  r : R x0 y0
  a : All2 R l l'
  ============================
   ({| pr1 := [x]; pr2 := y |} = {| pr1 := x0 :: l; pr2 := y0 :: l' |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in ∑ y' : B, y = [y'] × R x y')


DEBUG:Going to execute:
repeat DepElim.simplify_one_dep_elim