Section sequence_of_coprimes.
Let seq_of_coprimes_lt n i j : i < j <= n -> is_gcd (1+i*fact n) (1+j*fact n) 1.

Theorem seq_of_coprimes n i j :
i <= n
-> j <= n
-> i <> j
-> is_gcd (1+i*fact n) (1+j*fact n) 1.