FDL > PVS > Graphs > ramsey new > r1 TCC2 > pf:r1 TCC2 > 1 > 1 > 1 (2 nodes)


Conclusion

-1. FORALL A:finite set[T], S:set[T] : subset?(S, A) IMPLIES is finite(S)
-2. subset?({n:T | vert(G!1)(n) AND (n /= choose[T](vert(G!1))) AND edge?[T](G!1)(choose[T](vert(G!1)), n)}, vert(G!1))

1. is finite[T](LET (v0:(vert(G!1)) ) = choose[T](vert(G!1)) IN
{n:T | vert(G!1)(n) AND (n /= v0) AND edge?[T](G!1)(v0, n)})


Tactic
INST?

Premise 1.   (has proof of 1 step)

-1. subset?({n:T | vert(G!1)(n) AND (n /= choose[T](vert(G!1))) AND edge?[T](G!1)(choose[T](vert(G!1)), n)}, vert(G!1)) IMPLIES is finite({n:T | vert(G!1)(n) AND (n /= choose[T](vert(G!1))) AND edge?[T](G!1)(choose[T](vert(G!1)), n)})
-2. subset?({n:T | vert(G!1)(n) AND (n /= choose[T](vert(G!1))) AND edge?[T](G!1)(choose[T](vert(G!1)), n)}, vert(G!1))

1. is finite[T](LET (v0:(vert(G!1)) ) = choose[T](vert(G!1)) IN
{n:T | vert(G!1)(n) AND (n /= v0) AND edge?[T](G!1)(v0, n)})