
theorem
  for G1, G2 being _Graph, F being continuous PGraphMapping of G1, G2
  st F_E is one-to-one holds F is semi-continuous
proof
  let G1, G2 be _Graph;
  let F be continuous PGraphMapping of G1, G2;
  assume A1: F_E is one-to-one;
  let e,v,w be object;
  assume that
    A2: e in dom F_E & v in dom F_V & w in dom F_V and
    A3: F_E.e Joins F_V.v, F_V.w, G2;
  consider e0 being object such that
    A4: e0 Joins v,w,G1 & e0 in dom F_E & F_E.e0 = F_E.e by A2, A3, Def16;
  thus e Joins v,w,G1 by A1, A2, A4, FUNCT_1:def 4;
end;
