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 parallelogram a,b,c,d ; :: thesis: parallelogram c,d,a,b
then ( not c,d,a is_collinear & a,b // c,d & a,c // b,d ) by Def3, Th56;
then ( not c,d,a is_collinear & c,d // a,b & c,a // d,b ) by Th17;
hence parallelogram c,d,a,b by Def3; :: thesis: verum