FDL > PVS > Number Theory > gcd > gcd is max > pf:gcd_is_max : proof (11 nodes)


Conclusion

1. FORALL i:int, j:int, kk:nzint : (((i /= 0) OR (j /= 0)) AND divides(kk, i) AND divides(kk, j)) IMPLIES (kk < = gcd(i, j))


Tactic
SKOSIMP*

Premise 1.   (has proof of 10 steps)

-1. (i!1 /= 0) OR (j!1 /= 0)
-2. divides(kk!1, i!1)
-3. divides(kk!1, j!1)

1. kk!1 < = gcd(i!1, j!1)