Recall from Theorem 3 that there is a sequence (an) of elements of U that is cofinal in M.
Altering finitely many terms of the sequence (un) does not affect the validity of (9).
Let (an) be the sequence of zeros of f arranged so that |a1|≤|a2|≤......
Extend this sequence of numbers backwards, defining N-1, N-2 and N-3 by......
Then the sequence (8) breaks off in split exact sequences.
Thus the long exact sequence breaks up into short sequences.
The exact sequence ends on the right with H(X).
The proof proper [= The actual proof] will consist of establishing the following statements in sequence.
the all-one sequence