reserve i,j for Nat;

theorem Th26:
  for A,B,C being Matrix of REAL st len C = len A & width C =
width A & for i,j st [i,j] in Indices A holds C*(i,j) = A*(i,j) + B*(i,j) holds
  C=A+B
proof
  let A,B,C be Matrix of REAL;
  assume that
A1: len C =len A & width C=width A and
A2: for i,j holds [i,j] in Indices A implies C*(i,j) = A*(i,j) + B*(i,j);
  set B2=MXR2MXF B;
  set A2=MXR2MXF A;
  set D=MXR2MXF C;
  for i,j st [i,j] in Indices A2 holds D*(i,j) = A2*(i,j) + B2*(i,j) by A2;
  hence thesis by A1,MATRIX_3:def 3;
end;
