let SAS be Semi_Affine_Space; :: thesis: for a, b, c, d being Element of SAS st parallelogram a,b,c,d holds
not a,d // b,c
let a, b, c, d be Element of SAS; :: thesis: ( parallelogram a,b,c,d implies not a,d // b,c )
assume A1: parallelogram a,b,c,d ; :: thesis: not a,d // b,c
then not a,b,c are_collinear ;
then A2: not a,b // a,c ;
( a,b // c,d & a,c // b,d ) by A1;
hence not a,d // b,c by A2, Def1; :: thesis: verum