:: deftheorem Def4 defines Vars QC_LANG3:def 4 :
for A being QC-alphabet
for V being non empty Subset of (QC-variables A)
for p being Element of QC-WFF A
for b₄ being Subset of V holds
( b₄ = Vars (p,V) iff ex F being Function of (QC-WFF A),(bool V) st
( b₄ = F . p & ( for p being Element of QC-WFF A
for d1, d2 being Subset of V holds
( ( p = VERUM A implies F . p = {} V ) & ( p is atomic implies F . p = variables_in ((the_arguments_of p),V) ) & ( p is negative & d1 = F . (the_argument_of p) implies F . p = d1 ) & ( p is conjunctive & d1 = F . (the_left_argument_of p) & d2 = F . (the_right_argument_of p) implies F . p = d1 \/ d2 ) & ( p is universal & d1 = F . (the_scope_of p) implies F . p = d1 ) ) ) ) );