(** An example where a complex sequence of constructions is compiled into higher level constructions to ease the elimination process *)

(* Specifications: *)
Lemma example_construction_simplification:
forall A B C D E F G Line_3_b Line_6_b,
on_line C A B ->
on_parallel Line_3_b C A D ->
inter_ll E C Line_3_b B D ->
on_parallel Line_6_b C F A ->
inter_ll G C Line_6_b F B  ->
parallel E G D F.
Theorem parallellogram_construction_2 :
forall A B C D I : Point,
is_midpoint I A C ->
on_line_d D I B (-(1)) ->
parallel C D A B /\ parallel A D B C.