now :: thesis: ( not 2 divides 79 & not 3 divides 79 & not 5 divides 79 & not 7 divides 79 )

79 = (2 * 39) + 1 ;
hence not 2 divides 79 by NAT_4:9; :: thesis: ( not 3 divides 79 & not 5 divides 79 & not 7 divides 79 )
79 = (3 * 26) + 1 ;
hence not 3 divides 79 by NAT_4:9; :: thesis: ( not 5 divides 79 & not 7 divides 79 )
79 = (5 * 15) + 4 ;
hence not 5 divides 79 by NAT_4:9; :: thesis: not 7 divides 79
79 = (7 * 11) + 2 ;
hence not 7 divides 79 by NAT_4:9; :: thesis: verum

end;

then for n being Element of NAT st 1 < n & n * n <= 79 & n is prime holds
not n divides 79 by XPRIMET1:8;
hence 79 is prime by NAT_4:14; :: thesis: verum