theorem :: MSUALG_3:24

for S being non empty non void ManySortedSign
for U1, U2 being MSAlgebra over S
for o being OperSymbol of S
for F being ManySortedFunction of U1,U2
for x being Element of Args (o,U1)
for f, u being Function st x = f & x in Args (o,U1) & u in Args (o,U2) holds
( u = F # x iff for n being Nat st n in dom f holds
u . n = (F . ((the_arity_of o) /. n)) . (f . n) ) by Lm1;