22 0. Prequel M or lives in Int M, and exactly as in the initial case, either ht(Dt+1) ⊂ U1 or ht(Dt+1) ⊂ U2 in either event Jt is mapped by ht to a loop nullhomotopic in U0, implying the existence of the required map ht+1. As ∪k i=1 (Int Di) ⊃ h−1(A2), the final map hk : I2 → X has image in U1 = X A2, so it provides the desired path homotopy in U1 between α and the constant path.
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