reserve k,m,n for Element of NAT,
  i, j for Nat,
  a, b, c for object,
  X, Y, Z for set,
  D, D1, D2 for non empty set;
reserve p, q, r, s for FinSequence;
reserve t, u, v, w for GRZ-formula;
reserve R, R1, R2 for GRZ-rule;
reserve A, A1, A2 for non empty Subset of GRZ-formula-set;
reserve B, B1, B2 for Subset of GRZ-formula-set;
reserve P, P1, P2 for GRZ-formula-sequence;
reserve S, S1, S2 for GRZ-formula-finset;

theorem Th80:
  for t, u holds t LD-= u iff LD-EqClassOf t = LD-EqClassOf u
proof
  let t, u;
  thus t LD-= u implies LD-EqClassOf t = LD-EqClassOf u
    proof
    assume t LD-= u;
    then [t, u] in LD-EqR by Def80;
    then u in LD-EqClassOf t by EQREL_1:18;
    hence thesis by EQREL_1:23;
    end;
  assume LD-EqClassOf t = LD-EqClassOf u;
  then u in LD-EqClassOf t by EQREL_1:23;
  then [t, u] in LD-EqR by EQREL_1:18;
  hence thesis by Def80;
end;
