let a, I be set ; :: thesis: ex A being ManySortedSet of I st {A} = I --> {a}
reconsider A = I --> a as ManySortedSet of I ;
take A ; :: thesis: {A} = I --> {a}

now :: thesis: for i being object st i in I holds
{A} . i = (I --> {a}) . i

let i be object ; :: thesis: ( i in I implies {A} . i = (I --> {a}) . i )
assume A1: i in I ; :: thesis: {A} . i = (I --> {a}) . i
hence {A} . i = {(A . i)} by PZFMISC1:def 1
.= {a} by A1, FUNCOP_1:7
.= (I --> {a}) . i by A1, FUNCOP_1:7 ;
:: thesis: verum

end;

hence {A} = I --> {a} ; :: thesis: verum