theorem Th3:
((I,u)-TermEval.(m+1)).t =
(I.(S-firstChar.t)).(((I,u)-TermEval.m)*(SubTerms(t))) &
(t is 0-termal implies ((I,u)-TermEval.(m+1)).t = (I.(S-firstChar.t)).{})
proof
reconsider mm=m as Element of NAT by ORDINAL1:def 12;
((I,u)-TermEval.(mm+1)).t =
(I.(S-firstChar.t)).(((I,u)-TermEval.mm)*(SubTerms(t))) &
(t is 0-termal implies ((I,u)-TermEval.(mm+1)).t = (I.(S-firstChar.t)).{})
by Lm5;
hence thesis;
end;
