let SAS be Semi_Affine_Space; :: thesis: for a, b, c, d being Element of SAS st congr a,b,c,d & not a,b,c is_collinear holds
parallelogram a,b,c,d
let a, b, c, d be Element of SAS; :: thesis: ( congr a,b,c,d & not a,b,c is_collinear implies parallelogram a,b,c,d )
assume that
A1: congr a,b,c,d and
A2: not a,b,c is_collinear ; :: thesis: parallelogram a,b,c,d
( a,b // c,d & a,c // b,d ) by A1, Th76, Th77;
hence parallelogram a,b,c,d by A2, Def3; :: thesis: verum