let z1, z2 be Quaternion; :: thesis: |.z1.| - |.z2.| <= |.(z1 - z2).|
z1 = (z1 - z2) + z2 by Lm35;
then |.z1.| <= |.(z1 - z2).| + |.z2.| by Th72;
hence |.z1.| - |.z2.| <= |.(z1 - z2).| by XREAL_1:20; :: thesis: verum