
theorem
Sierp36 888,24
proof
  thus Sum digits(888,10) = 24 by Th1073;
  888=37*24;
  hence 24 divides 888 by INT_1:def 3;
  let m be Nat;
  assume A1: Sum digits(m,10) = 24 & 24 divides m;
  then consider j being Nat such that
  A2: m=24*j by NAT_D:def 3;
  assume m < 888;
  then 24*j < 24*37 by A2;
  then j < 36+1 by XREAL_1:64;
  then j <= 36 by NAT_1:9;
  then j=0 or ... or j=36;
  then per cases;
  suppose j=0;
    then Sum digits(m,10) = 0 by A2,Th6;
    hence contradiction by A1;
  end;
  suppose j=1;
    then Sum digits(m,10) = 6 by A2,Th95;
    hence contradiction by A1;
  end;
  suppose j=2;
    then Sum digits(m,10) = 12 by A2,Th99;
    hence contradiction by A1;
  end;
  suppose j=3;
    then Sum digits(m,10) = 9 by A2,Th273;
    hence contradiction by A1;
  end;
  suppose j=4;
    then Sum digits(m,10) = 15 by A2,Th185;
    hence contradiction by A1;
  end;
  suppose j=5;
    then Sum digits(m,10) = 3 by A2,Th39;
    hence contradiction by A1;
  end;
  suppose j=6;
    then Sum digits(m,10) = 9 by A2,Th189;
    hence contradiction by A1;
  end;
  suppose j=7;
    then Sum digits(m,10) = 15 by A2,Th153;
    hence contradiction by A1;
  end;
  suppose j=8;
    then Sum digits(m,10) = 12 by A2,Th191;
    hence contradiction by A1;
  end;
  suppose j=9;
    then Sum digits(m,10) = 9 by A2,Th1049;
    hence contradiction by A1;
  end;
  suppose j=10;
    then Sum digits(m,10) = 6 by A2,Th193;
    hence contradiction by A1;
  end;
  suppose j=11;
    then Sum digits(m,10) = 12 by A2,Th751;
    hence contradiction by A1;
  end;
  suppose j=12;
    then Sum digits(m,10) = 18 by A2,Th199;
    hence contradiction by A1;
  end;
  suppose j=13;
    then Sum digits(m,10) = 6 by A2,Th1051;
    hence contradiction by A1;
  end;
  suppose j=14;
    then Sum digits(m,10) = 12 by A2,Th205;
    hence contradiction by A1;
  end;
  suppose j=15;
    then Sum digits(m,10) = 9 by A2,Th371;
    hence contradiction by A1;
  end;
  suppose j=16;
    then Sum digits(m,10) = 15 by A2,Th211;
    hence contradiction by A1;
  end;
  suppose j=17;
    then Sum digits(m,10) = 12 by A2,Th258;
    hence contradiction by A1;
  end;
  suppose j=18;
    then Sum digits(m,10) = 9 by A2,Th217;
    hence contradiction by A1;
  end;
  suppose j=19;
    then Sum digits(m,10) = 15 by A2,Th314;
    hence contradiction by A1;
  end;
  suppose j=20;
    then Sum digits(m,10) = 12 by A2,Th379;
    hence contradiction by A1;
  end;
  suppose j=21;
    then Sum digits(m,10) = 9 by A2,Th1053;
    hence contradiction by A1;
  end;
  suppose j=22;
    then Sum digits(m,10) = 15 by A2,Th767;
    hence contradiction by A1;
  end;
  suppose j=23;
    then Sum digits(m,10) = 12 by A2,Th958;
    hence contradiction by A1;
  end;
  suppose j=24;
    then Sum digits(m,10) = 18 by A2,Th1055;
    hence contradiction by A1;
  end;
  suppose j=25;
    then Sum digits(m,10) = 6 by A2,Th391;
    hence contradiction by A1;
  end;
  suppose j=26;
    then Sum digits(m,10) = 12 by A2,Th1057;
    hence contradiction by A1;
  end;
  suppose j=27;
    then Sum digits(m,10) = 18 by A2,Th1059;
    hence contradiction by A1;
  end;
  suppose j=28;
    then Sum digits(m,10) = 15 by A2,Th1061;
    hence contradiction by A1;
  end;
  suppose j=29;
    then Sum digits(m,10) = 21 by A2,Th1063;
    hence contradiction by A1;
  end;
  suppose j=30;
    then Sum digits(m,10) = 9 by A2,Th403;
    hence contradiction by A1;
  end;
  suppose j=31;
    then Sum digits(m,10) = 15 by A2,Th1065;
    hence contradiction by A1;
  end;
  suppose j=32;
    then Sum digits(m,10) = 21 by A2,Th1067;
    hence contradiction by A1;
  end;
  suppose j=33;
    then Sum digits(m,10) = 18 by A2,Th789;
    hence contradiction by A1;
  end;
  suppose j=34;
    then Sum digits(m,10) = 15 by A2,Th1069;
    hence contradiction by A1;
  end;
  suppose j=35;
    then Sum digits(m,10) = 12 by A2,Th413;
    hence contradiction by A1;
  end;
  suppose j=36;
    then Sum digits(m,10) = 18 by A2,Th1071;
    hence contradiction by A1;
  end;
end;
