let FdSp be FanodesSp; :: thesis: for a, b, c, d being Element of FdSp st parallelogram a,b,c,d holds
not a,d '||' b,c
let a, b, c, d be Element of FdSp; :: thesis: ( parallelogram a,b,c,d implies not a,d '||' b,c )
assume A1: parallelogram a,b,c,d ; :: thesis: not a,d '||' b,c
then not a,b,c are_collinear ;
then A2: not a,b '||' a,c ;
( a,b '||' c,d & a,c '||' b,d ) by A1;
then not b,c '||' a,d by A2, Def1;
hence not a,d '||' b,c by PARSP_1:19; :: thesis: verum