still working towards isretr

homotopy/pointed_cubes.hlean

@@ -108,6 +108,34 @@ begin
   exact psq,
 end
 
+definition p2homotopy_ty_respect_pt {A B : Type*} {f g : A →* B} {H K : f ~* g} (htpy : H ~ K) : Type :=
+  begin
+    induction H with H p, exact p
+  end  = whisker_right (respect_pt g) (htpy pt) ⬝  
+  begin
+induction K with K q, exact q
+  end
+
+print p2homotopy_ty_respect_pt
+
+structure p2homotopy {A B : Type*} {f g : A →* B} (H K : f ~* g) : Type :=
+( to_2htpy : H ~ K)
+( respect_pt  : p2homotopy_ty_respect_pt to_2htpy)
+
+definition phsquare_of_p2homotopy {A B : Type*} {f g h i : A →* B} {phtpy_top : f ~* g} {phtpy_bot : h ~* i} {phtpy_left : f ~* h} {phtpy_right : g ~* i} (p2htpy : p2homotopy (phtpy_top ⬝* phtpy_right) (phtpy_left ⬝* phtpy_bot)) : phsquare phtpy_top phtpy_bot phtpy_left phtpy_right :=
+begin
+  induction p2htpy,
+  induction phtpy_left using phomotopy_rec_on_idp,
+  induction phtpy_right using phomotopy_rec_on_idp,
+  repeat exact sorry
+end
+
+definition ptube_v_phtpy_bot {A B C D : Type*} {ftop ftop' : A →* B} {phtpy_top : ftop ~* ftop'} {fbot fbot' fbot'' : C →* D} {phtpy_bot : fbot ~* fbot'} {phtpy_bot' : fbot' ~* fbot''} {fleft : A →* C} {fright : B →* D} {psq_back : psquare ftop fbot fleft fright} {psq_front : psquare ftop' fbot' fleft fright} {psq_front' : psquare ftop' fbot'' fleft fright} (ptb : ptube_v phtpy_top phtpy_bot psq_back psq_front) (ptb' : ptube_v phomotopy.rfl phtpy_bot' psq_front psq_front') : ptube_v phtpy_top (phtpy_bot ⬝* phtpy_bot') psq_back psq_front' :=
+begin
+  unfold ptube_v,
+  unfold phsquare
+end
+
 definition ptube_v_left_inv {A B C D : Type*} {ftop : A ≃* B} {fbot : C ≃* D} {fleft : A →* C} {fright : B →* D} 
   (psq : psquare ftop fbot fleft fright) : 
   ptube_v