reserve V for RealLinearSpace;
reserve u,u1,u2,v,v1,v2,w,w1,y for VECTOR of V;
reserve a,a1,a2,b,b1,b2,c1,c2 for Real;
reserve x,z for set;
reserve p,p1,q,q1 for Element of Lambda(OASpace(V));
reserve POS for non empty ParOrtStr;
reserve p,p1,p2,q,q1,r,r1,r2 for Element of AMSpace(V,w,y);

theorem Th36:
  for a,b,c,d being Element of POS, a9,b9,c9,d9 being Element of
  the AffinStruct of POS st a=a9& b=b9 & c = c9 & d=d9
   holds (a,b // c,d iff a9,b9 // c9,d9)
proof
  set AF = the AffinStruct of POS;
  let a,b,c,d be Element of POS, a9,b9,c9,d9 be Element of the AffinStruct of
  POS such that
A1: a=a9 & b=b9 & c = c9 & d=d9;
  hereby
    assume a,b // c,d;
    then [[a9,b9],[c9,d9]] in the CONGR of AF by A1,ANALOAF:def 2;
    hence a9,b9 // c9,d9 by ANALOAF:def 2;
  end;
  assume a9,b9 // c9,d9;
  then [[a,b],[c,d]] in the CONGR of POS by A1,ANALOAF:def 2;
  hence thesis by ANALOAF:def 2;
end;
