\r
ptU : U = (X : U) * X\r
\r
-lemPt1 (A :U) : (B:U) (p:Id U A B) (a:A) -> Id ptU (A,a) (B,transport p a)\r
- = J U A (\ (B:U) (p:Id U A B) -> (a:A) -> Id ptU (A,a) (B,transport p a))\r
- (\ (a:A) -> refl ptU (A,a))\r
-\r
-s1PtCircle1 : Id ptU (sone,north) (S1,base) = lemPt1 sone S1 s1EqCircle north\r
-\r
lemPt (A :U) (B:U) (p:Id U A B) (a:A) : Id ptU (A,a) (B,transport p a) =\r
<i> (p @ i,transport (<j>p @ (i/\j)) a)\r
\r
rem : G (S1,base) = winding\r
rem1 : G (sone,north) = subst ptU G (S1,base) (sone,north) (<i> s1PtCircle @ -i) rem\r
\r
-windingT : loopS1 -> Z = rem1\r
- where\r
- G (X: ptU): U = (Omega X).1 -> Z\r
- rem : G (S1,base) = winding\r
- rem1 : G (S1,base) = subst ptU G (S1,base) (S1,base) s1PtS1 rem\r
-\r
s1ToCId (p: Id sone north north) : Id S1 base base\r
= <i> transport s1EqCircle (p @ i) \r
\r
\r
test2S : Z = windingS loop2S\r
\r
-winding' (l : Id sone north north) : Z = winding (s1ToCId l)\r
-\r
-testS : Id sone north north = <i> comp sone (m0 @ i) [ (i=1) -> <k> m1 @ (-k)]\r