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