reserve E,V for set, G,G1,G2 for _Graph, c,c1,c2 for Cardinal, n for Nat;
reserve f for VColoring of G;
reserve g for EColoring of G;
reserve t for TColoring of G;

theorem Th140:
  for v,x being object, G1 being addVertex of G2,v, t being TColoring of G2
  holds [t_V +* (v .--> x), t_E] is TColoring of G1
proof
  let v,x be object, G1 be addVertex of G2,v, t be TColoring of G2;
  A1: dom(v .--> x) = dom{[v,x]} by FUNCT_4:82
    .= {v} by RELAT_1:9;
  dom(t_V +* (v .--> x)) = dom t_V \/ dom(v .--> x) by FUNCT_4:def 1
    .= the_Vertices_of G2 \/ {v} by A1, PARTFUN1:def 2
    .= the_Vertices_of G1 by GLIB_006:def 10;
  then A2: t_V+*(v.-->x) is VColoring of G1 by RELAT_1:def 18, PARTFUN1:def 2;
  the_Edges_of G1 = the_Edges_of G2 by GLIB_006:def 10;
  hence thesis by A2, Def9;
end;
