reserve i,j for Nat;

theorem Th36:
  for n,m being Nat,A being Matrix of REAL st len A=n & width A=m
  & n>0 holds A+ 0_Rmatrix(n,m)=A & 0_Rmatrix(n,m)+A=A
proof
  let n,m be Nat,A be Matrix of REAL;
  assume that
A1: len A=n & width A=m and
A2: n>0;
  reconsider D=MXR2MXF A as Matrix of n,m,F_Real by A1,A2,MATRIX_0:20;
  len (0.(F_Real,n,m))=n & width (0.(F_Real,n,m))=m by A2,MATRIX_0:23;
  then
A3: 0_Rmatrix(n,m)+A=MXF2MXR (D+0.(F_Real,n,m)) by A1,MATRIX_3:2
    .=A by MATRIX_3:4;
  MXR2MXF A is Matrix of n,m,F_Real by A1,A2,MATRIX_0:20;
  hence thesis by A3,MATRIX_3:4;
end;
