
theorem Th43: :: VAdjacent00
  for G1,G2 being _Graph st G1 == G2 for u1,v1 being Vertex of G1
st u1,v1 are_adjacent for u2,v2 being Vertex of G2 st u1=u2 & v1=v2 holds u2,v2
  are_adjacent
proof
  let G1,G2 be _Graph such that
A1: G1 == G2;
  let u1,v1 be Vertex of G1;
  assume u1,v1 are_adjacent;
  then consider e being object such that
A2: e Joins u1,v1,G1;
  let u2,v2 be Vertex of G2 such that
A3: u1=u2 and
A4: v1=v2;
  e Joins u2,v2,G2 by A1,A3,A4,A2;
  hence thesis;
end;
