let p be Element of CQC-WFF ; :: thesis: for x being Element of bound_QC-variables holds QuantNbr (All (x,p)) = (QuantNbr p) + 1
let x be Element of bound_QC-variables ; :: thesis: QuantNbr (All (x,p)) = (QuantNbr p) + 1
A1: for p being Element of CQC-WFF
for d being Element of NAT holds
( d = H₅(p) iff 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 k
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) ) ) ) ) by Def5;
thus H₅( All (x,p)) = H₄(x,H₅(p)) from CQC_LANG:sch 9(A1); :: thesis: verum