
theorem
Sierp36 266,14
proof
  thus Sum digits(266,10) = 14 by Th165;
  266=19*14;
  hence 14 divides 266 by INT_1:def 3;
  let m be Nat;
  assume A1: Sum digits(m,10) = 14 & 14 divides m;
  then consider j being Nat such that
  A2: m=14*j by NAT_D:def 3;
  assume m < 266;
  then 14*j < 14*19 by A2;
  then j < 18+1 by XREAL_1:64;
  then j <= 18 by NAT_1:9;
  then j=0 or ... or j=18;
  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) = 5 by A2,Th137;
    hence contradiction by A1;
  end;
  suppose j=2;
    then Sum digits(m,10) = 10 by A2,Th139;
    hence contradiction by A1;
  end;
  suppose j=3;
    then Sum digits(m,10) = 6 by A2,Th141;
    hence contradiction by A1;
  end;
  suppose j=4;
    then Sum digits(m,10) = 11 by A2,Th143;
    hence contradiction by A1;
  end;
  suppose j=5;
    then Sum digits(m,10) = 7 by A2,Th29;
    hence contradiction by A1;
  end;
  suppose j=6;
    then Sum digits(m,10) = 12 by A2,Th145;
    hence contradiction by A1;
  end;
  suppose j=7;
    then Sum digits(m,10) = 17 by A2,Th147;
    hence contradiction by A1;
  end;
  suppose j=8;
    then Sum digits(m,10) = 4 by A2,Th149;
    hence contradiction by A1;
  end;
  suppose j=9;
    then Sum digits(m,10) = 9 by A2,Th151;
    hence contradiction by A1;
  end;
  suppose j=10;
    then Sum digits(m,10) = 5 by A2,Th43;
    hence contradiction by A1;
  end;
  suppose j=11;
    then Sum digits(m,10) = 10 by A2,Th80;
    hence contradiction by A1;
  end;
  suppose j=12;
    then Sum digits(m,10) = 15 by A2,Th153;
    hence contradiction by A1;
  end;
  suppose j=13;
    then Sum digits(m,10) = 11 by A2,Th124;
    hence contradiction by A1;
  end;
  suppose j=14;
    then Sum digits(m,10) = 16 by A2,Th155;
    hence contradiction by A1;
  end;
  suppose j=15;
    then Sum digits(m,10) = 3 by A2,Th157;
    hence contradiction by A1;
  end;
  suppose j=16;
    then Sum digits(m,10) = 8 by A2,Th159;
    hence contradiction by A1;
  end;
  suppose j=17;
    then Sum digits(m,10) = 13 by A2,Th161;
    hence contradiction by A1;
  end;
  suppose j=18;
    then Sum digits(m,10) = 9 by A2,Th163;
    hence contradiction by A1;
  end;
end;
