reserve U0 for Universal_Algebra,
  U1 for SubAlgebra of U0,
  o for operation of U0;

theorem
  for H being non empty Subset of U0 for o holds H is_closed_on o &
  arity o = 0 implies (o/.H) = o
proof
  let H be non empty Subset of U0;
  let o;
  assume that
A1: H is_closed_on o and
A2: arity o = 0;
A3: dom o = 0 -tuples_on the carrier of U0 by A2,MARGREL1:22
    .= { <*>the carrier of U0 } by FINSEQ_2:94
    .= { <*>H }
    .= 0 -tuples_on H by FINSEQ_2:94;
  o/.H = o|(0 -tuples_on H) by A1,A2,UNIALG_2:def 5;
  hence thesis by A3,RELAT_1:69;
end;
