Goal:
  
  A : Type
  B : Type
  R : A → B → Type
  x : A
  y0 : B
  l' : list B
  r : R x y0
  a1' : list A
  a1 : list B
  a : All2 R (pr1 {| pr1 := a1'; pr2 := a1 |})
        (pr2 {| pr1 := a1'; pr2 := a1 |})
  ============================
   ({| pr1 := []; pr2 := l' |} = {| pr1 := a1'; pr2 := a1 |}
    → let H := CoreTactics.block in
      let H0 := CoreTactics.block in ∑ y' : B, y0 :: l' = [y'] × R x y')


DEBUG:Going to execute:
match type of id with
           | sigma _ =>
               let xn := fresh id "'" in
               destruct id as [xn id]; DepElim.decompose_exists xn id;
                cbv beta iota delta [TODO projection TODO projection]
                 in id, id'; DepElim.decompose_exists id id'
           | _ =>
               cbv beta iota delta [TODO projection TODO projection]
                in id, id'
           end