let A be QC-alphabet ; :: thesis: for t being QC-symbol of A
for q, p being Element of CQC-WFF A
for f being Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
for K being Finite_Subset of (bound_QC-variables A) st [q,t,K,f] in SepQuadruples p holds
not x. t in f .: (still_not-bound_in q)
let t be QC-symbol of A; :: thesis: for q, p being Element of CQC-WFF A
for f being Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
for K being Finite_Subset of (bound_QC-variables A) st [q,t,K,f] in SepQuadruples p holds
not x. t in f .: (still_not-bound_in q)
let q, p be Element of CQC-WFF A; :: thesis: for f being Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
for K being Finite_Subset of (bound_QC-variables A) st [q,t,K,f] in SepQuadruples p holds
not x. t in f .: (still_not-bound_in q)
let f be Element of Funcs ((bound_QC-variables A),(bound_QC-variables A)); :: thesis: for K being Finite_Subset of (bound_QC-variables A) st [q,t,K,f] in SepQuadruples p holds
not x. t in f .: (still_not-bound_in q)
let K be Finite_Subset of (bound_QC-variables A); :: thesis: ( [q,t,K,f] in SepQuadruples p implies not x. t in f .: (still_not-bound_in q) )
assume A1: [q,t,K,f] in SepQuadruples p ; :: thesis: not x. t in f .: (still_not-bound_in q)
assume x. t in f .: (still_not-bound_in q) ; :: thesis: contradiction
then ( t < t & t <= t ) by A1, Th42, QC_LANG1:22;
hence contradiction by QC_LANG1:25; :: thesis: verum