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 for I being Element of U-InterpretersOf S holds
I-TruthEval phi=1 iff {phi} is I-satisfied
proof
let I be Element of U-InterpretersOf S;
thus I-TruthEval phi=1 implies {phi} is I-satisfied by TARSKI:def 1;
assume {phi} is I-satisfied; then reconsider X={phi} as I-satisfied set;
phi in X by TARSKI:def 1; hence I-TruthEval phi=1 by Def41;
end;
