let T be non empty arcwise_connected TopSpace; :: thesis: for a1, b1, c1 being Point of T
for A1, A2 being Path of a1,b1
for B being Path of c1,a1 st A1,A2 are_homotopic holds
A1,((- B) + B) + A2 are_homotopic
let a1, b1, c1 be Point of T; :: thesis: for A1, A2 being Path of a1,b1
for B being Path of c1,a1 st A1,A2 are_homotopic holds
A1,((- B) + B) + A2 are_homotopic
( a1,b1 are_connected & c1,a1 are_connected ) by BORSUK_2:def 3;
hence for A1, A2 being Path of a1,b1
for B being Path of c1,a1 st A1,A2 are_homotopic holds
A1,((- B) + B) + A2 are_homotopic by Th24; :: thesis: verum