let k be Element of NAT ; :: thesis: for p being QC-pred_symbol of k
for ll being QC-variable_list of
for e being Element of vSUB holds [(<*p*> ^ ll),e] in [:([:NAT ,NAT :] * ),vSUB :]
let p be QC-pred_symbol of k; :: thesis: for ll being QC-variable_list of
for e being Element of vSUB holds [(<*p*> ^ ll),e] in [:([:NAT ,NAT :] * ),vSUB :]
let ll be QC-variable_list of ; :: thesis: for e being Element of vSUB holds [(<*p*> ^ ll),e] in [:([:NAT ,NAT :] * ),vSUB :]
( k -ary_QC-pred_symbols c= [:NAT ,NAT :] & QC-variables c= [:NAT ,NAT :] ) by QC_LANG1:4, QC_LANG1:10, XBOOLE_1:1;
then ( rng <*p*> c= [:NAT ,NAT :] & rng ll c= [:NAT ,NAT :] ) by XBOOLE_1:1;
then (rng <*p*>) \/ (rng ll) c= [:NAT ,NAT :] by XBOOLE_1:8;
then rng (<*p*> ^ ll) c= [:NAT ,NAT :] by FINSEQ_1:44;
then <*p*> ^ ll is FinSequence of [:NAT ,NAT :] by FINSEQ_1:def 4;
then <*p*> ^ ll in [:NAT ,NAT :] * by FINSEQ_1:def 11;
hence for e being Element of vSUB holds [(<*p*> ^ ll),e] in [:([:NAT ,NAT :] * ),vSUB :] by ZFMISC_1:def 2; :: thesis: verum