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