let n be even Nat; :: thesis: ( not n <= 5 or n = 0 or n = 2 or n = 4 )
assume A1: n <= 5 ; :: thesis: ( n = 0 or n = 2 or n = 4 )
n <> (2 * 2) + 1 ;
then n < 4 + 1 by A1, XXREAL_0:1;
then A2: n <= 4 by NAT_1:13;

per cases ( n = 4 or n < 3 + 1 ) by A2, XXREAL_0:1;

suppose n = 4 ; :: thesis: ( n = 0 or n = 2 or n = 4 )

hence ( n = 0 or n = 2 or n = 4 ) ; :: thesis: verum

end;

suppose n < 3 + 1 ; :: thesis: ( n = 0 or n = 2 or n = 4 )

then n <= 3 by NAT_1:13;
hence ( n = 0 or n = 2 or n = 4 ) by Th11; :: thesis: verum

end;

end;