Section Grad.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

(* Specifications: *)
Lemma grad__bet : forall A B C, Grad A B C -> Bet A B C.
Lemma grad__col : forall A B C, Grad A B C -> Col A B C.
Lemma grad_neq__neq13 : forall A B C, Grad A B C -> A <> B -> A <> C.
Lemma grad_neq__neq12 : forall A B C, Grad A B C -> A <> C -> A <> B.
Lemma grad112__eq : forall A B, Grad A A B -> A = B.
Lemma grad121__eq : forall A B, Grad A B A -> A = B.
Lemma grad__le : forall A B C, Grad A B C -> Le A B A C.
Lemma grad2__grad123 : forall A B C D E F, Grad2 A B C D E F -> Grad A B C.
Lemma grad2__grad456 : forall A B C D E F, Grad2 A B C D E F -> Grad D E F.
Lemma grad_sum : forall A B C D E,
Grad A B C -> Grad A B D -> Bet A C E -> Cong A D C E ->
Grad A B E.
Lemma gradexp__grad : forall A B C, GradExp A B C -> Grad A B C.
Lemma gradexp_le__reach : forall A B C D B',
GradExp A B B' -> Le C D A B' ->
Reach A B C D.
Lemma grad__ex_gradexp_le : forall A B C,
Grad A B C ->
exists D, GradExp A B D /\ Le A C A D.
Lemma reach__ex_gradexp_le : forall A B C D, Reach A B C D ->
exists B', GradExp A B B' /\ Le C D A B'.
Lemma gradexp2__gradexp123 : forall A B C D E F,
GradExp2 A B C D E F ->
GradExp A B C.
Lemma gradexp2__gradexp456 : forall A B C D E F,
GradExp2 A B C D E F ->
GradExp D E F.