theorem :: MONOID_1:57

for G being non empty multMagma holds

( ( G is commutative implies bool G is commutative ) & ( G is associative implies bool G is associative ) & ( G is uniquely-decomposable implies bool G is uniquely-decomposable ) )

( ( G is commutative implies bool G is commutative ) & ( G is associative implies bool G is associative ) & ( G is uniquely-decomposable implies bool G is uniquely-decomposable ) )