(* Specifications: *)
Lemma FunSET_map_law1 : Map_law FunSET_mor1.
Lemma Inc_comp_law : Fcomp_law Inc_map.
Lemma Inc_id_law : Fid_law Inc_map.
Lemma Comp_Functor_congl : Congl_law' Comp_Functor.
Lemma Comp_Functor_congr : Congr_law' Comp_Functor.
Lemma Functor_preserves_iso : forall (F : Functor C D) (a b : C), Iso a b -> Iso (F a) (F b).
Lemma FunForget_map_law : Map_law (MonMap (m1:=m1) (m2:=m2)).
Lemma Fst_map_law : forall a b : PROD A B, Map_law (Hom_l (u:=a) (t:=b)).
Lemma Ast_eq : forall a : A, FMor F' (T a) o T' (G a) =_S T' (F a) o FMor G' (T a).
Lemma Ast_nt_law : NT_law Ast.
Lemma NtH_map_law : Map_law NtH_arrow.
Lemma FunY_map_law : Map_law0'' (NtH (C:=C) (b:=a) (a:=b)).
Lemma Comp_map_congl : Congl_law Comp_map.
Lemma Comp_map_congr : Congr_law Comp_map.
Lemma Idl_inv : forall i : Iso, RIso_law (Iso_mor i) (Inv_iso i).
Lemma Idr_inv : forall i : Iso, RIso_law (Inv_iso i) (Iso_mor i).
Lemma Inv_iso_unique : forall f g : Iso, Iso_mor f =_S Iso_mor g -> Inv_iso f =_S Inv_iso g.
Lemma UniqueI : forall (i : Initial) (b : C), At_most_1mor (Initial_ob i) b.
Lemma I_unic : forall i1 i2 : Initial, Iso (Initial_ob i1) (Initial_ob i2).
Lemma UniqueT : forall (t : Terminal) (a : C), At_most_1mor a (Terminal_ob t).
Lemma Codiese_map : forall a' : A, Map_law (CoUA_diese t (a':=a')).
Lemma Diese_map : forall a' : A, Map_law (UA_diese t (a':=a')).
Lemma Comp_cone_tau_cone_law : Cone_law Comp_cone_tau.
Lemma Lp_sigma_tau_cone_law : Cone_law Lp_sigma_tau.
Lemma FT_cd2_law : h =_S f i o FMor G t.
Theorem Rstar_reflexive : forall (U : Type) (R : Relation U), Reflexive (Rstar R).
Theorem Rplus_contains_R : forall (U : Type) (R : Relation U), Contains (Rplus R) R.
Theorem Rstar_contains_R : forall (U : Type) (R : Relation U), Contains (Rstar R) R.
Theorem Rstar_contains_Rplus : forall (U : Type) (R : Relation U), Contains (Rstar R) (Rplus R).
Theorem Rstar_transitive : forall (U : Type) (R : Relation U), Transitive (Rstar R).
Theorem Rstar_cases : forall (U : Type) (R : Relation U) (x y : U), Rstar R x y -> x = y \/ (exists u : U, R x u /\ Rstar R u y).
Theorem Rstar_equiv_Rstar1 : forall (U : Type) (R : Relation U), Same_relation (Rstar R) (Rstar1 R).
Theorem Rsym_imp_Rstarsym : forall (U : Type) (R : Relation U), Symmetric R -> Symmetric (Rstar R).
Theorem Sstar_contains_Rstar : forall (U : Type) (R S : Relation U), Contains (Rstar S) R -> Contains (Rstar S) (Rstar R).
Theorem star_monotone : forall (U : Type) (R S : Relation U), Contains S R -> Contains (Rstar S) (Rstar R).
Theorem RstarRplus_RRstar : forall (U : Type) (R : Relation U) (x y z : U), Rstar R x y -> Rplus R y z -> exists u : U, R x u /\ Rstar R u z.
Theorem Rstar_imp_coherent : forall (U : Type) (R : Relation U) (x y : U), Rstar R x y -> coherent R x y.
Theorem coherent_symmetric : forall (U : Type) (R : Relation U), Symmetric (coherent R).
Theorem Newman : forall (U : Type) (R : Relation U), Noetherian R -> Locally_confluent R -> Confluent R.
Theorem Strip : forall (U : Type) (R : Relation U), Strongly_confluent R -> forall x b : U, Rstar R x b -> forall a : U, R x a -> exists z : U, Rstar R a z /\ R b z.
Theorem Strong_confluence_confluence : forall (U : Type) (R : Relation U), Strongly_confluent R -> Confluent R.