reserve x for set,
  R for non empty Poset;
reserve S1 for OrderSortedSign,
  OU0 for OSAlgebra of S1;
reserve s,s1,s2,s3,s4 for SortSymbol of S1;
reserve U0 for non-empty OSAlgebra of S1;

theorem Th46:
  OSAlg_meet(U0) is commutative
proof
  set o = OSAlg_meet(U0);
  set m = MSAlg_meet(U0);
A1: m is commutative by MSUALG_2:31;
  for x,y be Element of OSSub(U0) holds o.(x,y)=o.(y,x)
  proof
    let x,y be Element of OSSub(U0);
    o.(x,y) = m.(x,y) by Th43
      .= m.(y,x) by A1,BINOP_1:def 2
      .= o.(y,x) by Th43;
    hence thesis;
  end;
  hence thesis by BINOP_1:def 2;
end;
