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 parallelogram a,b,c,d ; :: thesis: not a,d // b,c
then ( not a,b,c is_collinear & a,b // c,d & a,c // b,d ) by Def3;
then ( not a,b // a,c & a,b // c,d & a,c // b,d ) by Def2;
hence not a,d // b,c by Def1; :: thesis: verum