reserve T for BinContinuous unital TopSpace-like non empty TopGrStr,
  x,y for Point of I[01],
  s,t for unital Point of T,
  f,g for Loop of t,
  c for constant Loop of t;

theorem Th11:
  f+g = LoopMlt(f+c,c+g)
  proof
    let x;
A1: c = I --> t by BORSUK_2:5;
    now per cases;
      suppose
A2:     x <= 1/2;
        then reconsider z = 2*x as Point of I by BORSUK_6:3;
A3:     (f+c).x = f.z by A2,BORSUK_2:def 5;
        (c+g).x = c.z by A2,BORSUK_2:def 5
        .= t by A1;
        hence (f+g).x = (f+c).x * (c+g).x by A2,A3,BORSUK_2:def 5;
      end;
      suppose
A4:     x >= 1/2;
        then reconsider z = 2*x-1 as Point of I by BORSUK_6:4;
A5:     (f+c).x = c.z by A4,BORSUK_2:def 5
        .= t by A1;
        (c+g).x = g.z by A4,BORSUK_2:def 5;
        hence (f+g).x = (f+c).x * (c+g).x by A5,A4,BORSUK_2:def 5;
      end;
    end;
    hence thesis by Def2;
  end;
