Proof [x:A]
[hyp_ind:(u:A)
(R x u)->(y:A)(z:A)(Rstar u y)->(Rstar u z)->(coherence y z)]
[y,z:A]
[h1:(Rstar x y)]
[h2:(Rstar x z)]
[u:A]
[t1:(R x u)]
[t2:(Rstar u y)]
(unf_Rstar' [P:A->A->Prop](P x z)->(coherence y z)
[hyp_:(P:A->A->Prop)
(P x x)
->((u0:A)(R x u0)->(Rstar u0 z)->(P x z))->(P x z)]
(hyp_ [_:A][a:A](coherence y a)
(coherence_sym x y (Rstar_coherence x y h1))
(Diagram x hyp_ind y z u t1 t2))
(Rstar_Rstar' x z h2)).

Theorem Ind_proof : (x:A)
((u:A)
(R x u)
->(y:A)(z:A)(Rstar u y)->(Rstar u z)->(coherence y z))
->(y:A)(z:A)(Rstar x y)->(Rstar x z)->(coherence y z).