let a, b be Point of T; ( R62(T,a,b) implies R62(T,b,a) )
set P = the Path of a,b;
assume A1:
a,b are_connected
; R62(T,b,a)
then A2:
the Path of a,b . 1 = b
by BORSUK_2:def 2;
take
- the Path of a,b
; BORSUK_2:def 1 ( - the Path of a,b is continuous & (- the Path of a,b) . 0 = b & (- the Path of a,b) . 1 = a )
( the Path of a,b is continuous & the Path of a,b . 0 = a )
by A1, BORSUK_2:def 2;
hence
( - the Path of a,b is continuous & (- the Path of a,b) . 0 = b & (- the Path of a,b) . 1 = a )
by A2, Th41; verum