reserve a,b for Real,
  i,j,n for Nat,
  M,M1,M2,M3,M4 for Matrix of n, REAL;

theorem
  a>=0 & b>=0 & M1 is Nonnegative & M2 is Nonnegative implies a*M1+b*M2
  is Nonnegative
proof
  assume a>=0 & b>=0 & M1 is Nonnegative & M2 is Nonnegative;
  then a*M1 is Nonnegative & b*M2 is Nonnegative by Th42;
  hence thesis by Th36;
end;
