now :: thesis:

let Seqts1, Seqts2 be Subset of (S -sequents); :: thesis:
let f be Function; :: thesis:
assume A1: ( Seqts1 c= Seqts2 & f in {M} ) ; :: thesis:
then reconsider F = f as isotone Rule of S by TARSKI:def 1;
take g = f; :: thesis:
thus g in {M} by A1; :: thesis:
F . Seqts1 c= F . Seqts2 by A1, Def10;
hence f . Seqts1 c= g . Seqts2 ; :: thesis:

end;

hence for b₁ being RuleSet of S st b₁ = {M} holds
b₁ is isotone ; :: thesis: