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