theorem Th13: :: PRALG_3:13

for S being non empty non void ManySortedSign
for o being OperSymbol of S
for U1, U2 being non-empty MSAlgebra over S
for F being ManySortedFunction of U1,U2
for x being Element of Args (o,U1)
for n being set st n in dom (the_arity_of o) holds
(F # x) . n = (F . ((the_arity_of o) /. n)) . (x . n)