defpred S1[ Nat] means (MycielskianSeq G) . G is finite ;
A1: S1[ 0 ] by Th113;
A2: now :: thesis: for k being Nat st S1[k] holds
S1[k + 1]
let k be Nat; :: thesis: ( S1[k] implies S1[k + 1] )
assume A3: S1[k] ; :: thesis: S1[k + 1]
set H = (MycielskianSeq G) . k;
(MycielskianSeq G) . (k + 1) = Mycielskian ((MycielskianSeq G) . k) by Th115;
hence S1[k + 1] by A3; :: thesis: verum
end;
for k being Nat holds S1[k] from NAT_1:sch 2(A1, A2);
 hence (MycielskianSeq G) . n is finite ; :: thesis: verum