Homotopy paths

[valtz]

i stuck when i want to prove theorem 51.3 in munkres 2en editions about homotopy paths

Let f be a path in X , and let a0 , .... , an be numbers such that 0= a0 < a1 < ... < an. Let fi : I → X be the path that equals the positive linear map of I onto [ai-1, ai] followed by f then

[f] = [f1] * ..... * [fn]


any idea to start prove this theorems?

[mathwonk]

draw a picture.