let A, B be ManySortedFunction of OSFreeGen X, PTVars X; :: thesis: ( ( for s being Element of S holds A . s = NHReverse s,X ) & ( for s being Element of S holds B . s = NHReverse s,X ) implies A = B )
assume that
A4: for s being Element of S holds A . s = NHReverse s,X and
A5: for s being Element of S holds B . s = NHReverse s,X ; :: thesis: A = B
for i being set st i in the carrier of S holds
A . i = B . i

proof

let i be set ; :: thesis: ( i in the carrier of S implies A . i = B . i )
assume i in the carrier of S ; :: thesis: A . i = B . i
then reconsider s = i as SortSymbol of S ;
( A . s = NHReverse s,X & B . s = NHReverse s,X ) by A4, A5;
hence A . i = B . i ; :: thesis: verum

end;

hence A = B by PBOOLE:3; :: thesis: verum