let n be Nat; :: thesis: for z, z1, z2 being Element of COMPLEX n holds |.(z1 - z2).| <= |.(z1 - z).| + |.(z - z2).|
let z, z1, z2 be Element of COMPLEX n; :: thesis: |.(z1 - z2).| <= |.(z1 - z).| + |.(z - z2).|
|.(z1 - z2).| = |.(((z1 - z) + z) - z2).| by Th80
.= |.((z1 - z) + (z - z2)).| by Th75 ;
hence |.(z1 - z2).| <= |.(z1 - z).| + |.(z - z2).| by Th97; :: thesis: verum