L l c x = y = c avec x place d'apres l l = liste de chemins dans l'arbre c = arbre [V,V,F] Kab=a, Ka=L[]a, K=L[] Sabc=ac(bc) S=L[[F]](L[F,F]] ( L[[V],[F]])) transym a=c, b=c -> a=b egap f=g, a=b -> fa=gb a = Ia a = Kab ac(bc) = Sabc I=I K=K S=S S E! I = KI ... -> Kab = a -> Sabc = ac(bc) |- p -> |- V=p |- V=p -> |- p |- x, |- x=y -> |- y |- f=g -> |- fx=gx [fg] (f=g) = [x](fx=gx) [xy] (x=y) = [f] (fx=fy) [xy] (V=(x=y)) \/ (F=(x=y)) [x] x=x [xy] (x=y) = (y=x) [xyz] ((x=y) => (y=z) => (x=z)) |- V=px, |- F=py -> |- F=(x=y) |- F=(px=py) -> |- F=(x=y) |- [fg] f=g => [x] fx=gx (x) |- [fg] (f=g => (fx=gx)) |- [pxy] (((V=(x=y)) => p) => (((F=(x=y)) => p) => p)) |-pV, |-pF -> [xy] p(x=y) |- [xy] (x=y) = [z] (y=z) = (x=z) -> Kab = a -> Sabc = ac(bc) |- p -> |- V=p |- V=p -> |- p |- x, |- x=y -> |- y |- f=g -> |- fx=gx [fg] (f=g) = [x](fx=gx) [xy] (x=y) = [f] (fx=fy) [xy] (V=(x=y)) \/ (F=(x=y)) [x] x=x [xy] (x=y) = (y=x) [xyz] ((x=y) => (y=z) => (x=z)) fX=gX, X ... f Xi, Xi pas dans f -> KV = f (x=y)