let SAS be Semi_Affine_Space; :: thesis: for a, b, c, d being Element of SAS st parallelogram a,b,c,d holds
parallelogram c,d,a,b
let a, b, c, d be Element of SAS; :: 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 Th17;
a,c // b,d by A1, Def3;
then A3: c,a // d,b by Th17;
not c,d,a is_collinear by A1, Th56;
hence parallelogram c,d,a,b by A2, A3, Def3; :: thesis: verum