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- { x = n , n > 0 }
- { x = n , n > 0 , 0 = 0 }
- z := 0;
- { x = n , n > z , z = 0 }
- { x = n , n > z , z = 0 , 1 = 1 }
- odd := 1;
- { x = n , n > z , z = 0 , odd = 1 }
- { x = n , n > z , z = 0 , odd = 1 , 1 = 1}
- sum := 1;
- { x = n , n > z , z = 0 , odd = sum , sum = 1 }
- { x = n , n > z , z = 0 , odd = sum - 0 , sum = 1 }
- { x = n , n > z , z = 0 , odd = sum - (z ^ 2) , sum = 1 }
- { x = n , n > z , z = 0 , sum - odd = (z ^ 2) , sum = (z + 1) ^ 2 , sum <= x } = INV
- while sum <= x
- { sum <= x ^ INV }
- z := z + 1;
- odd := odd + 2;
- sum := sum + odd;
- { ¬(sum <= x) , INV }
- { sum > x , INV }
- { }
- { (z ^ 2) <= n , (z + 1) ^ 2 > n }
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