reserve T for non empty TopSpace,
  a, b, c, d for Point of T;
reserve X for non empty pathwise_connected TopSpace,
  a1, b1, c1, d1 for Point of X;

theorem Th82:
  for P be Path of a, b, Q be constant Path of a, a st a, b
  are_connected holds Q + P, P are_homotopic
proof
  let P be Path of a, b, Q be constant Path of a, a such that
A1: a,b are_connected;
  RePar (P, 2RP) = Q + P by A1,Th51;
  hence thesis by A1,Th45,Th48;
end;
