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

now :: thesis: for i being object st i in I holds
(union {A,B}) . i = (A (\/) B) . i

let i be object ; :: 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_1:75
.= (A (\/) B) . i by A1, PBOOLE:def 4 ;
:: thesis: verum

end;

hence union {A,B} = A (\/) B ; :: thesis: verum