let A be QC-alphabet ; :: thesis: for t being QC-symbol of A
for p, q being Element of CQC-WFF A
for f being Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
for K being Element of Fin (bound_QC-variables A) st [q,t,K,f] in SepQuadruples p holds
not x. t in f .: K
let t be QC-symbol of A; :: thesis: for p, q being Element of CQC-WFF A
for f being Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
for K being Element of Fin (bound_QC-variables A) st [q,t,K,f] in SepQuadruples p holds
not x. t in f .: K
let p, q be Element of CQC-WFF A; :: thesis: for f being Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
for K being Element of Fin (bound_QC-variables A) st [q,t,K,f] in SepQuadruples p holds
not x. t in f .: K
let f be Element of Funcs ((bound_QC-variables A),(bound_QC-variables A)); :: thesis: for K being Element of Fin (bound_QC-variables A) st [q,t,K,f] in SepQuadruples p holds
not x. t in f .: K
let K be Element of Fin (bound_QC-variables A); :: thesis: ( [q,t,K,f] in SepQuadruples p implies not x. t in f .: K )
assume A1: [q,t,K,f] in SepQuadruples p ; :: thesis: not x. t in f .: K
assume x. t in f .: K ; :: thesis: contradiction
then ( t < t & t <= t ) by A1, Th39, QC_LANG1:22;
hence contradiction by QC_LANG1:25; :: thesis: verum