
theorem Th60:
  for G1, G2 being _Graph, F being PGraphMapping of G1, G2
  st F is Disomorphism holds
    G1.supInDegree() = G2.supInDegree() &
    G1.supOutDegree() = G2.supOutDegree() &
    G1.minInDegree() = G2.minInDegree() &
    G1.minOutDegree() = G2.minOutDegree()
proof
  let G1, G2 be _Graph, F be PGraphMapping of G1, G2;
  assume A1: F is Disomorphism;
  then A2: dom F_V = the_Vertices_of G1 & rng F_V = the_Vertices_of G2
    by GLIB_010:def 11, GLIB_010:def 12;
  A3: G1.supInDegree() c= G2.supInDegree() &
    G1.supOutDegree() c= G2.supOutDegree() by A1, Th56;
  A4: G1.minInDegree() c= G2.minInDegree() &
    G1.minOutDegree() c= G2.minOutDegree() by A1, A2, Th57;
  A5: G2.supInDegree() c= G1.supInDegree() &
    G2.supOutDegree() c= G1.supOutDegree() by A1, Th58;
  A6: G2.minInDegree() c= G1.minInDegree() &
    G2.minOutDegree() c= G1.minOutDegree() by A1, A2, Th59;
  thus thesis by A3, A4, A5, A6, XBOOLE_0:def 10;
end;
