thus ( ex d being Element of NAT ex F being Function of CQC-WFF ,NAT st
( d = F . p & F . VERUM = 0 & ( for r, s being Element of CQC-WFF
for x being Element of bound_QC-variables
for k being Element of NAT
for l being CQC-variable_list of
for P being QC-pred_symbol of k holds
( F . (P ! l) = H₁(k,P,l) & F . ('not' r) = H₂(F . r) & F . (r '&' s) = H₃(F . r,F . s) & F . (All x,r) = H₄(x,F . r) ) ) ) & ( for d1, d2 being Element of NAT st ex F being Function of CQC-WFF ,NAT st
( d1 = F . p & F . VERUM = 0 & ( for r, s being Element of CQC-WFF
for x being Element of bound_QC-variables
for k being Element of NAT
for l being CQC-variable_list of
for P being QC-pred_symbol of k holds
( F . (P ! l) = H₁(k,P,l) & F . ('not' r) = H₂(F . r) & F . (r '&' s) = H₃(F . r,F . s) & F . (All x,r) = H₄(x,F . r) ) ) ) & ex F being Function of CQC-WFF ,NAT st
( d2 = F . p & F . VERUM = 0 & ( for r, s being Element of CQC-WFF
for x being Element of bound_QC-variables
for k being Element of NAT
for l being CQC-variable_list of
for P being QC-pred_symbol of k holds
( F . (P ! l) = H₁(k,P,l) & F . ('not' r) = H₂(F . r) & F . (r '&' s) = H₃(F . r,F . s) & F . (All x,r) = H₄(x,F . r) ) ) ) holds
d1 = d2 ) ) from CQC_LANG:sch 4(); :: thesis: verum