formal proof of how this algorithm is correct?

bool isSubsequence(string sequence, string subsequence) {
	/*
	Objective : To check for subsequence in a given string
	Input parameters: sequence - string, sequence S
	subsequence - string, subsequence S'
	Return Value : true, if subsequence found
	otherwise, false
	*/
	int n = sequence.length(); //length of sequence
	int m = subsequence.length(); //length of subsequence
	int j = 0;
	//for loop till length of sequence
	for(int i = 0; i < n; ++i) {
	//break if all chars of subsequence are checked
	if(j == m) {
	break;
	}
	//increment j if subsequence[j] is equal to sequence[i]
	if(subsequence[j] == sequence[i]) {
	j++;
	}
	}
	//subsequence found if j is equal to length of subsequence
	if(j == m) {
	return true ;
	}
	return false;
	}