let FdSp be FanodesSp; :: thesis: for a, b, c, d being Element of FdSp st parallelogram a,b,c,d holds
parallelogram c,d,a,b
let a, b, c, d be Element of FdSp; :: thesis: ( parallelogram a,b,c,d implies parallelogram c,d,a,b )
assume A1: parallelogram a,b,c,d ; :: thesis: parallelogram c,d,a,b
then a,b '||' c,d by Def3;
then A2: c,d '||' a,b by PARSP_1:23;
a,c '||' b,d by A1, Def3;
then A3: c,a '||' d,b by PARSP_1:23;
not c,d,a is_collinear by A1, Th36;
hence parallelogram c,d,a,b by A2, A3, Def3; :: thesis: verum