
theorem lemgcd0a:
for R being gcdDomain
for a being Element of R holds a is a_gcd of a,0.R
proof
let R be gcdDomain, a be Element of R;
A: a divides a;
   a * 0.R = 0.R; then
B: a divides 0.R by GCD_1:def 1;
for r being Element of R st r divides a & r divides 0.R holds r divides a;
hence thesis by A,B,RING_4:def 10;
end;
