theorem Th81:
  for p holds for v,vS,vS1,vS2 st (for y st y in dom vS1 holds not
y in still_not-bound_in p) & (for y st y in dom vS2 holds vS2.y = v.y) & dom vS
  misses dom vS2 holds J,v.vS |= p iff J,v.(vS+*vS1+*vS2) |= p
proof
  defpred P[Element of CQC-WFF(Al)] means for v,vS,vS1,vS2 st
   (for y st y in dom vS1 holds not y in still_not-bound_in $1) &
   (for y st y in dom vS2 holds vS2.y = v.y) & dom vS misses dom vS2 holds
    J,v.vS |= $1 iff J,v.(vS+*vS1+*vS2) |= $1;
A1: for p,q,x,k for l being CQC-variable_list of k,Al for P being
QC-pred_symbol of k,Al holds P[VERUM(Al)] & P[P!l] & (P[p] implies P['not' p])
 & (P[p] & P[q] implies P[p '&' q]) & (P[p] implies P[All(x,p)])
  by Th75,Th76,Th77,Th80,VALUAT_1:32;
  thus for p holds P[p] from CQC_LANG:sch 1(A1);
end;
