Definition plusTerm : Term -> Term -> Term.

(* Specifications: *)
Theorem zeroP_plusTermr : forall a b : Term, eqT a b -> zeroP b -> eqTerm a (plusTerm a b).
Theorem zeroP_plusTerml : forall a b : Term, eqT a b -> zeroP a -> eqTerm b (plusTerm a b).
Theorem plusTerm_comp_l : forall a b c : Term, eqT a c -> eqT b c -> eqTerm a b -> eqTerm (plusTerm a c) (plusTerm b c).
Theorem plusTerm_comp_r : forall a b c : Term, eqT c a -> eqT c b -> eqTerm a b -> eqTerm (plusTerm c a) (plusTerm c b).
Theorem plusTerm_com : forall x y : Term, eqT x y -> eqTerm (plusTerm x y) (plusTerm y x).
Theorem plusTerm_eqT1 : forall m1 m2 : Term, eqT m1 m2 -> eqT (plusTerm m1 m2) m1.
Theorem plusTerm_eqT2 : forall m1 m2 : Term, eqT m1 m2 -> eqT (plusTerm m1 m2) m2.
Theorem plusTerm_assoc : forall a a0 A1 : Term, eqT A1 a0 -> eqT a a0 -> eqTerm (plusTerm (plusTerm A1 a0) a) (plusTerm A1 (plusTerm a0 a)).
Theorem eqTerm_plusTerm_comp : forall a b c d : Term, eqT a c -> eqT b d -> eqTerm a b -> eqTerm c d -> eqTerm (plusTerm a c) (plusTerm b d).