:: deftheorem defines is_homomorphism MSUALG_3:def 7 :
for S being non empty non void ManySortedSign
for U1, U2 being MSAlgebra over S
for F being ManySortedFunction of U1,U2 holds
( F is_homomorphism U1,U2 iff for o being OperSymbol of S st Args (o,U1) <> {} holds
for x being Element of Args (o,U1) holds (F . (the_result_sort_of o)) . ((Den (o,U1)) . x) = (Den (o,U2)) . (F # x) );