FDL > PVS > Number Theory > gcd > gcd TCC1 > pf:gcd_TCC1 : proof (4 nodes)


Conclusion

1. FORALL i:int, j:{jj:int | (i = 0) = > (jj /= 0)} : nonempty?[posnat]({k:posnat | divides(k, i) AND divides(k, j)}) AND (EXISTS UB : FORALL y:({k:posnat | divides(k, i) AND divides(k, j)}) : y < = UB)


Tactic
SKOSIMP*

Premise 1.   (has proof of 3 steps)

1. nonempty?[posnat]({k:posnat | divides(k, i!1) AND divides(k, j!1)}) AND (EXISTS UB : FORALL y:({k:posnat | divides(k, i!1) AND divides(k, j!1)}) : y < = UB)