for S being non empty non void ManySortedSign
for X being V5() ManySortedSet of the carrier of S
for o being OperSymbol of S
for p being DTree-yielding FinSequence st [o, the carrier of S] -tree p in the Sorts of (FreeMSA X) . (the_result_sort_of o) holds
for i being Nat st i in dom (the_arity_of o) holds
p . i in the Sorts of (FreeMSA X) . ((the_arity_of o) . i)