
theorem Th25: :: Path01
  for G being _Graph, P being Path of G, m, n being odd Nat
  st m <= len P & n <= len P & P.m = P.n holds m = n or m = 1 & n = len P
  or m = len P & n = 1
proof
  let G be _Graph, P be Path of G, m, n be odd Nat such that
A1: m <= len P and
A2: n <= len P and
A3: P.m = P.n;
A4: m in NAT by ORDINAL1:def 12;
A5: n in NAT by ORDINAL1:def 12;
  m=n or m<n or n<m by XXREAL_0:1;
  hence thesis by A1,A2,A3,A4,A5,GLIB_001:def 28;
end;
