let S be non empty non void ManySortedSign ; :: thesis: for U1 being non-empty MSAlgebra over S
for f being Element of MSAAut U1 holds
( f is "1-1" & f is "onto" )
let U1 be non-empty MSAlgebra over S; :: thesis: for f being Element of MSAAut U1 holds
( f is "1-1" & f is "onto" )
let f be Element of MSAAut U1; :: thesis: ( f is "1-1" & f is "onto" )
f is_isomorphism U1,U1 by Def5;
hence ( f is "1-1" & f is "onto" ) by MSUALG_3:13; :: thesis: verum