# pre-conditions-start

Requires(n >= 0)

# pre-conditions-end

# post-conditions-start

Ensures(Result() >= 0)

Ensures((Result()) == fizz_buzz_fun(n))

# post-conditions-end

# impl-start

result : int = 0

d_1_i_ : int = 0

while (d_1_i_) < (n):

# invariants-start

Invariant(((0) <= (d_1_i_)) and ((d_1_i_) <= (n)))

Invariant(Forall(int, lambda x : (Implies(x >= 0 and x < n,

fizz_buzz_fun(x + 1) == (count7__r(x) if ((x % 11 == 0) or (x % 13 == 0)) else 0) + fizz_buzz_fun(x)), [[fizz_buzz_fun(x + 1)]])))

Invariant(result == fizz_buzz_fun(d_1_i_))

# invariants-end

if (((d_1_i_ % 11)) == (0)) or (((d_1_i_ % 13)) == (0)):

d_4_cnt_ : int = count7(d_1_i_)

result = (result) + (d_4_cnt_)

d_1_i_ = (d_1_i_) + (1)

return result

# pre-conditions-start

Requires(n >= 0)

# pre-conditions-end

# post-conditions-start

Ensures(Result() >= 0)

# post-conditions-end

# pure-start

if n == 0:

return 0

else:

return (count7__r(n - 1) if ((n - 1) % 11 == 0 or (n - 1) % 13 == 0) else 0) + fizz_buzz_fun(n - 1)

# pre-conditions-start

Requires(x >= 0)

# pre-conditions-end

# post-conditions-start

Ensures(Result() >= 0)

Ensures((Result()) == (count7__r(x)))

# post-conditions-end

# impl-start

count : int = 0

d_6_y_ : int = x

while (d_6_y_) > (0):

# invariants-start

Invariant(((0) <= (d_6_y_)) and ((d_6_y_) <= (x)))

Invariant(((count) + (count7__r(d_6_y_))) == (count7__r(x)))

# invariants-end

if ((d_6_y_ % 10)) == (7):

count = (count) + (1)

d_6_y_ = d_6_y_ // 10

return count

# pre-conditions-start

Requires(x >= 0)

# pre-conditions-end

# post-conditions-start

Ensures(Result() >= 0)

# post-conditions-end

# pure-start

if x == 0:

return 0

else:

return (x % 10 == 7) + count7__r(x // 10)