set Q = S -sequents ;
set F = Funcs ((bool (S -sequents)),(bool (S -sequents)));
let IT1, IT2 be Rule of S; :: thesis:
reconsider IT11 = IT1, IT22 = IT2 as Function of (bool (S -sequents)),(bool (S -sequents)) ;
deffunc H₁( set ) -> set = union ((union D) .: {$1});
assume A2: for Seqs being Element of bool (S -sequents) holds IT1 . Seqs = H₁(Seqs) ; :: thesis:
assume A3: for Seqs being Element of bool (S -sequents) holds IT2 . Seqs = H₁(Seqs) ; :: thesis:

let x be Element of bool (S -sequents); :: thesis:
thus IT11 . x = H₁(x) by A2
.= IT22 . x by A3 ; :: thesis:

end;