let T be non empty TopSpace; :: thesis: for a, b being Point of T
for P being Path of a,b
for Q being constant Path of a,a st a,b are_connected holds
Q + P,P are_homotopic
let a, b be Point of T; :: thesis: for P being Path of a,b
for Q being constant Path of a,a st a,b are_connected holds
Q + P,P are_homotopic
let P be Path of a,b; :: thesis: for Q being constant Path of a,a st a,b are_connected holds
Q + P,P are_homotopic
let Q be constant Path of a,a; :: thesis: ( a,b are_connected implies Q + P,P are_homotopic )
assume A1: a,b are_connected ; :: thesis: Q + P,P are_homotopic
RePar P,2RP = Q + P by A1, Th59;
hence Q + P,P are_homotopic by A1, Th53, Th56; :: thesis: verum