let I be set ; :: thesis: for A, B being ManySortedSet of holds union {A,B} = A \/ B
let A, B be ManySortedSet of ; :: thesis: union {A,B} = A \/ B

now

let i be set ; :: thesis: ( i in I implies (union {A,B}) . i = (A \/ B) . i )
assume A1: i in I ; :: thesis: (union {A,B}) . i = (A \/ B) . i
hence (union {A,B}) . i = union ({A,B} . i) by MBOOLEAN:def 2
.= union {(A . i),(B . i)} by A1, Def2
.= (A . i) \/ (B . i) by ZFMISC_1:93
.= (A \/ B) . i by A1, PBOOLE:def 7 ;
:: thesis: verum

end;

hence union {A,B} = A \/ B by PBOOLE:3; :: thesis: verum