:: deftheorem VFS defines vf-sequence MSAFREE5:def 42 :
for S being non empty non void ManySortedSign
for X being non-empty ManySortedSet of the carrier of S
for t being Element of (Free (S,X))
for b₄ being FinSequence holds
( b₄ is vf-sequence of t iff ex f being one-to-one FinSequence st
( rng f = { xi where xi is Element of dom t : ex s being SortSymbol of S ex x being Element of X . s st t . xi = [x,s] } & dom b₄ = dom f & ( for i being Nat st i in dom b₄ holds
b₄ . i = t . (f . i) ) ) );