Goal:
  
  A : Type
  sizeA : A → nat
  B : Type
  sizeB : B → nat
  a : A
  l : list A
  f : nat → A → B
  k : nat
  IHl : BinInt.Z.le (BinInt.Z.of_nat (list_size sizeB (mapi_rec f l (S k))))
          (BinInt.Z.of_nat (list_size sizeA l))
  H : BinInt.Z.le (BinInt.Z.of_nat (sizeB (f k a)))
        (BinInt.Z.of_nat (sizeA a))
  cstr : BinInt.Z.le BinNums.Z0 (BinInt.Z.of_nat (sizeA a))
  cstr0 : BinInt.Z.le BinNums.Z0 (BinInt.Z.of_nat (sizeB (f k a)))
  cstr1 : BinInt.Z.le BinNums.Z0 (BinInt.Z.of_nat (list_size sizeA l))
  cstr2 : BinInt.Z.le BinNums.Z0
            (BinInt.Z.of_nat (list_size sizeB (mapi_rec f l (S k))))
  ============================
   (BinInt.Z.le
      (BinInt.Z.add
         (BinInt.Z.add (BinInt.Z.of_nat (sizeB (f k a)))
            (BinInt.Z.of_nat (list_size sizeB (mapi_rec f l (S k)))))
         (BinNums.Zpos BinNums.xH))
      (BinInt.Z.add
         (BinInt.Z.add (BinInt.Z.of_nat (sizeA a))
            (BinInt.Z.of_nat (list_size sizeA l))) 
         (BinNums.Zpos BinNums.xH)))


DEBUG:Going to execute:
<coq-core.plugins.micromega::Lia@0> $1