Proposition 4

Let $C, C', D, D'$ be four complexes, $f : C \to C'$, $g : C \to C'$, $u : D \to C$, $v : C' \to D'$ four morphisms. If $s$ is a homotopy connecting $f$ to $g$, then $v \circ s \circ u$ is a homotopy connecting $v \circ f \circ u$ to $v \circ g \circ u$. If $f$ and $g$ are homotopic, then $v \circ f \circ u$ and $v \circ g \circ u$ are also homotopic. This is clear.