reserve V for RealLinearSpace;
reserve p,q,u,v,w,y for VECTOR of V;
reserve a,b,c,d for Real;

theorem Th2:
  y+u = v+w implies y-w = v-u
proof
  assume
A1: y+u=v+w;
  thus y-w = (y+0.V)-w by RLVECT_1:4
    .= (y+(u-u))-w by RLVECT_1:15
    .=((v+w)+(-u))-w by A1,RLVECT_1:def 3
    .= (-u)+((v+w)-w) by RLVECT_1:def 3
    .= v-u by RLSUB_2:61;
end;
