Ltac local_uniformize_signed_areas := Runiformize_signed_areas.(*
Ltac local_uniformize_signed_areas := uniformize_signed_areas.
*)

Ltac local_basic_simpl := Rbasic_simpl.Ltac local_uniformize_signed_areas4 := uniformize_signed_areas4.

(* Specifications: *)
Lemma test1 : forall A B C :Point, S A B C = S B C A.
Lemma test2 : forall A B C :Point, S A B C + S B A C = 0.
Lemma test3 : forall A B C :Point, S A B C + S A C B = 0.
Lemma test4 : forall A B C :Point, S A B C +- S B C A = 0.
Lemma test5 : forall A B C :Point, S A B C - S C A B = 0.
Lemma test6 : forall A B C :Point, S A B C + S C B A = 0.
Lemma test7 : forall A B C :Point, S A B C + S B A C = 0 -> 0=0.
Lemma test8 : forall A B C :Point, S A B C + S A C B = 0 -> 0=0.
Lemma test9 : forall A B C :Point, S A B C - S B C A = 0 -> 0=0.
Lemma test10 : forall A B C :Point, S A B C - S C A B = 0 -> 0=0.
Lemma test11 : forall A B C :Point, S A B C + S C B A = 0 -> 0=0.
Lemma test12 : forall A B C :Point, S A B C - S C A B = 0 -> S A B C + S C B A = 0.
Lemma test13 : forall A B C :Point, S A B C + S C B A = 0 -> S A B C + S B A C = 0 -> S A B C - S B C A = 0 .
Lemma test15 : forall A B C : Point, S A B C = 0 -> S B A C = 0.
Lemma test16 : forall A B C : Point, S A B C + S B A C = S A B C -> 0=0.
Lemma test172 : forall A B C, S A B C <> 0 -> S C B A = 0 -> S B C A =0 -> 0=1.
Lemma test173 : forall A B C P, - (S A C P / S B C P * (S B A P / S C A P * (S C B P / S A B P))) = 1 -> 0=0.
Lemma test174 : forall A B C P, S B C P <> 0 -> S A B P <> 0 -> S C A P <> 0 -> False -> - (S A C P / S B C P * (S B A P / S C A P * (S C B P / S A B P))) = 1.
Lemma test18 : forall A B C D, S4 A B C D = S4 B C D A.
Lemma test19 : forall A B C D, S4 A B C D = S4 C D A B.
Lemma test20 : forall A B C D, S4 A B C D = S4 D A B C.
Lemma test21 : forall A B C D, S4 A B C D = - S4 A D C B.
Lemma test22 : forall A B C D, S4 A B C D = - S4 D C B A.
Lemma test23 : forall A B C D, S4 A B C D = - S4 C B A D.
Lemma test24 : forall A B C D, S4 A B C D = - S4 B A D C.
Lemma test25 : forall A B C D, S4 A B C D = - S4 B A D C -> 0=0.
Lemma test26 : forall A B C D, S4 A B C D = - S4 B A D C -> S4 A B C D = - S4 B A D C.
Lemma test27 : forall A C D, S4 A A C D = 0 -> 0=0.
Lemma test28 : forall A C D, S4 C D A A = 0 -> 0=0.
Lemma test29 : forall A C D, S4 A C D A = 0 -> 0=0.
Lemma test30 : forall A C D, S4 C A A D = 0 -> 0=0.
Lemma test31 : forall A C D, S4 C A D A = 0 -> 0=0.
Lemma test32 : forall A C D, S4 A C A D = 0 -> 0=0.
Lemma test40 : forall A C, S A A C + S A C C + S A C A = 0.
Lemma test50 : forall A , A<>0 -> A/ A = 1.
Lemma test51 : forall A , A<>0 -> A/ A = 0 -> 0=1.
Lemma test53 : forall A, A<>0 -> (0+A)/A+(-A)/A=0.
Lemma test54 : forall x, -x*-x=x*x.
Lemma test55 : forall x y, -x*y=-(x*y).
Lemma test56 : forall x y, y<>0 -> (-x)/y=-(x/y).
Lemma test57 : forall y, y<>0 -> 0/y=0.
Lemma test58 : forall x y, y<>0 -> (x*y)/y =x.
Lemma test59 : forall x y, x<>0 -> (x*y)/x =y.
Lemma test60 : forall x y, x<>0 -> (x*y)/x =y -> 0=0.
Lemma test61 : forall A B C, False -> S A B C=0.
Lemma test62 : forall A B C, False -> 0 = S A B C.
Lemma test65 : forall A B C D E F:Point, S A C D <> 0 -> S B A F + S A B F = 0.