(* Constructions with lift_path *********************************************)
lemma lift_unwind2_rmap_after (g) (f) (p):
- ↑[⊗p]g∘▶[f]p ≗ ▶[g∘f]p.
+ 🠢[g]⊗p∘▶[f]p ≗ ▶[g∘f]p.
#g #f #p elim p -p //
* [ #k ] #p #IH //
[ <unwind2_rmap_d_dx <unwind2_rmap_d_dx
qed.
lemma unwind2_lift_rmap_after (g) (f) (p:path):
- ▶[g]↑[f]p∘↑[p]f ≗ ▶[g∘f]p.
+ ▶[g]🠡[f]p∘🠢[f]p ≗ ▶[g∘f]p.
#g #f #p elim p -p // #l #p #IH
<lift_path_rcons <lift_rmap_rcons <unwind2_rmap_rcons <unwind2_rmap_rcons
@(stream_eq_trans … (preunwind2_lift_rmap_after …))