let S be non empty non void ManySortedSign ; :: thesis: for U1 being non-empty MSAlgebra over S
for f1, f2 being Element of MSAAut U1 holds f1 ** f2 in MSAAut U1
let U1 be non-empty MSAlgebra over S; :: thesis: for f1, f2 being Element of MSAAut U1 holds f1 ** f2 in MSAAut U1
let f1, f2 be Element of MSAAut U1; :: thesis: f1 ** f2 in MSAAut U1
( f1 is_isomorphism U1,U1 & f2 is_isomorphism U1,U1 ) by Def5;
then f1 ** f2 is_isomorphism U1,U1 by MSUALG_3:15;
hence f1 ** f2 in MSAAut U1 by Def5; :: thesis: verum