let x1, x2, y1, y2 be Real; :: thesis: |[x1,y1]| - |[x2,y2]| = |[(x1 - x2),(y1 - y2)]|
A1: ( |[x2,y2]| `1 = x2 & |[x2,y2]| `2 = y2 ) by FINSEQ_1:44;
( |[x1,y1]| `1 = x1 & |[x1,y1]| `2 = y1 ) by FINSEQ_1:44;
hence |[x1,y1]| - |[x2,y2]| = |[(x1 - x2),(y1 - y2)]| by A1, Th33; :: thesis: verum