let m, n be Nat; :: thesis: ( not m * n = 10 or ( m = 1 & n = 10 ) or ( m = 2 & n = 5 ) or ( m = 5 & n = 2 ) or ( m = 10 & n = 1 ) )
assume A1: m * n = 10 ; :: thesis: ( ( m = 1 & n = 10 ) or ( m = 2 & n = 5 ) or ( m = 5 & n = 2 ) or ( m = 10 & n = 1 ) )
m divides m * n ;
then ( m = 1 or m = 2 or m = 5 or m = 10 ) by A1, Th12;
hence ( ( m = 1 & n = 10 ) or ( m = 2 & n = 5 ) or ( m = 5 & n = 2 ) or ( m = 10 & n = 1 ) ) by A1; :: thesis: verum