reserve k,m,n for Nat, kk,mm,nn for Element of NAT, A,B,X,Y,Z,x,y,z for set,
S, S1, S2 for Language, s for (Element of S), w,w1,w2 for (string of S),
U,U1,U2 for non empty set, f,g for Function, p,p1,p2 for FinSequence;
reserve u,u1,u2 for Element of U, t for termal string of S,
I for (S,U)-interpreter-like Function,
l, l1, l2 for literal (Element of S), m1, n1 for non zero Nat,
phi0 for 0wff string of S, psi,phi,phi1,phi2 for wff string of S;
reserve I for Element of U-InterpretersOf S;
reserve I for (S,U)-interpreter-like Function;

theorem Th24: for I being Element of U-InterpretersOf S holds
(I,m)-TruthEval in Funcs(S-formulasOfMaxDepth m, BOOLEAN)
proof
set Phim=S-formulasOfMaxDepth m, II=U-InterpretersOf S;
let I be Element of II; reconsider F=curry ((S,U)-TruthEval m) as Function of
II, Funcs(Phim, BOOLEAN) by Lm17; F.I in Funcs(Phim, BOOLEAN); hence thesis;
end;
