After j ranges from 1 to i, it will still be the case that the values from 1 to i are sorted. So you can assume that j starts at i without disturbing the induction condition.
The reason this is true is... If A[i] is >= any element A[j] for j < i, then it is clearly true. Otherwise, there is some smallest j in 1 to i-1 inclusive such that A[i] < A[j]. Then A[i] will swap with that A[j], then it will swap again with the next A[j+1] (because the original A[j] was < A[j+1]) by the induction case, then with the next element, ... swapping with every element until j reaches i.
After this is done we have maintained the condition that A[1] .. A[i] are sorted after j ranges from 1 to i.
