reserve F for Field;
reserve a,b,c,d,p,q,r for Element of MPS(F);
reserve e,f,g,h,i,j,k,l,m,n,o,w for Element of [:the carrier of F,the carrier
  of F,the carrier of F:];
reserve K,L,M,N,R,S for Element of F;
reserve FdSp for FanodesSp;
reserve a,b,c,d,p,q,r,s,o,x,y for Element of FdSp;

theorem Th35:
  parallelogram a,b,c,p & parallelogram a,b,c,q implies p=q
proof
  assume that
A1: parallelogram a,b,c,p and
A2: parallelogram a,b,c,q;
  a,b '||'c,p by A1;
  then
A3: b,c '||' c,b & b,a '||' c,p by PARSP_1:23,25;
  a,b '||' c,q by A2;
  then
A4: b,a '||' c,q by PARSP_1:23;
  a,c '||' b,p by A1;
  then
A5: c,a '||' b,p by PARSP_1:23;
  a,c '||' b,q by A2;
  then
A6: c,a '||' b,q by PARSP_1:23;
  not b,c,a are_collinear by A1,Th28;
  then not b,c '||' b,a;
  hence thesis by A3,A4,A5,A6,PARSP_1:34;
end;
