let n be odd Nat; :: thesis: ( not n <= 4 or n = 1 or n = 3 )
assume A1: n <= 4 ; :: thesis: ( n = 1 or n = 3 )
n <> 2 * 2 ;
then n < 3 + 1 by A1, XXREAL_0:1;
then A2: n <= 3 by NAT_1:13;

per cases ( n = 3 or n < 2 + 1 ) by A2, XXREAL_0:1;

suppose n = 3 ; :: thesis: ( n = 1 or n = 3 )

hence ( n = 1 or n = 3 ) ; :: thesis: verum

end;

suppose n < 2 + 1 ; :: thesis: ( n = 1 or n = 3 )

then n <= 2 by NAT_1:13;
hence ( n = 1 or n = 3 ) by Th6; :: thesis: verum

end;

end;