let n be even Nat; :: thesis: ( not n <= 7 or n = 0 or n = 2 or n = 4 or n = 6 )
assume A1: n <= 7 ; :: thesis: ( n = 0 or n = 2 or n = 4 or n = 6 )
n <> (2 * 3) + 1 ;
then n < 6 + 1 by A1, XXREAL_0:1;
then A2: n <= 6 by NAT_1:13;

per cases ( n = 6 or n < 5 + 1 ) by A2, XXREAL_0:1;

suppose n = 6 ; :: thesis: ( n = 0 or n = 2 or n = 4 or n = 6 )

hence ( n = 0 or n = 2 or n = 4 or n = 6 ) ; :: thesis: verum

end;

suppose n < 5 + 1 ; :: thesis: ( n = 0 or n = 2 or n = 4 or n = 6 )

then n <= 5 by NAT_1:13;
hence ( n = 0 or n = 2 or n = 4 or n = 6 ) by Th12; :: thesis: verum

end;

end;