diff --git a/algebra/exact_couple.hlean b/algebra/exact_couple.hlean
index 32833e1..1d4321c 100644
--- a/algebra/exact_couple.hlean
+++ b/algebra/exact_couple.hlean
@@ -5,7 +5,7 @@
 
 -- Author: Floris van Doorn
 
-import .graded ..spectrum.basic .product_group
+import .graded ..spectrum.basic .product_group .ring
 
 open algebra is_trunc left_module is_equiv equiv eq function nat sigma set_quotient group
      left_module
@@ -535,7 +535,8 @@ namespace exact_couple
 
   open int group prod convergence_theorem prod.ops
 
-  definition Z2 [constructor] : AddAbGroup := agℤ ×aa agℤ
+  local attribute [coercion] AddAbGroup_of_Ring
+  definition Z2 [constructor] : AddAbGroup := rℤ ×aa rℤ
 
   structure convergent_exact_couple.{u v w} {R : Ring} (E' : agℤ → agℤ → LeftModule.{u v} R)
                                  (Dinf : agℤ → LeftModule.{u w} R) : Type.{max u (v+1) (w+1)} :=
@@ -722,7 +723,7 @@ namespace spectrum
 
   definition i_sequence : D_sequence →gm D_sequence :=
   begin
-    fapply graded_hom.mk, exact (prod_equiv_prod erfl (add_right_action (- (1 : ℤ)))),
+    fapply graded_hom.mk, exact (prod_equiv_prod erfl (add_right_action (- 1))),
     { intro i, exact pair_eq !add_zero⁻¹ idp },
     intro v,
     apply lm_hom_int.mk, esimp,
@@ -730,7 +731,7 @@ namespace spectrum
   end
 
   definition deg_j_seq_inv [constructor] : I ≃ I :=
-  prod_equiv_prod (add_right_action (1 : ℤ)) (add_right_action (- (1 : ℤ)))
+  prod_equiv_prod (add_right_action 1) (add_right_action (- 1))
 
   definition fn_j_sequence [unfold 3] (x : I) :
     D_sequence (deg_j_seq_inv x) →lm E_sequence x :=
@@ -759,7 +760,7 @@ namespace spectrum
     intro y, induction x with n s, induction y with m t,
     refine equiv_rect !pair_eq_pair_equiv⁻¹ᵉ _ _,
     intro pq, esimp at pq, induction pq with p q,
-    revert t q, refine eq.rec_equiv (add_right_action (-(1 : ℤ))) _,
+    revert t q, refine eq.rec_equiv (add_right_action (- 1)) _,
     induction p using eq.rec_symm,
     apply is_exact_homotopy homotopy.rfl,
     { symmetry, exact graded_hom_mk_out_destruct deg_j_seq_inv⁻¹ᵉ (λi, idp) fn_j_sequence },
@@ -789,7 +790,7 @@ namespace spectrum
 
   open int
   parameters (ub : ℤ → ℤ) (lb : ℤ → ℤ)
-    (Aub : Π(s n : ℤ), s ≥ ub n + (1 : ℤ) → is_equiv (πₛ→[n] (f s)))
+    (Aub : Π(s n : ℤ), s ≥ ub n + 1 → is_equiv (πₛ→[n] (f s)))
     (Alb : Π(s n : ℤ), s ≤ lb n → is_contr (πₛ[n] (A s)))
 
   definition B : I → ℕ
@@ -799,7 +800,7 @@ namespace spectrum
   | (n, s) := max0 (ub n - s)
 
   definition B'' : I → ℕ
-  | (n, s) := max0 (max (ub n + (1 : ℤ) - s) (ub (n+(1 : ℤ)) + (1 : ℤ) - s))
+  | (n, s) := max0 (max (ub n + 1 - s) (ub (n+1) + 1 - s))
 
   lemma iterate_deg_i (n s : ℤ) (m : ℕ) : (deg i_sequence)^[m] (n, s) = (n, s - m) :=
   begin
@@ -862,7 +863,7 @@ namespace spectrum
     { intro n, change max0 (ub n - ub n) = 0, exact ap max0 (sub_self (ub n)) },
     { intro ns, reflexivity },
     { intro n, reflexivity },
-    { intro r, exact (-(1 : ℤ), r + (1 : ℤ)) },
+    { intro r, exact (- 1, r + 1) },
     { intro r, refine !convergence_theorem.deg_dr ⬝ _,
       refine ap (deg j_sequence) !iterate_deg_i_inv ⬝ _,
       exact prod_eq idp !zero_add }
diff --git a/algebra/ring.hlean b/algebra/ring.hlean
index be89caf..97ee0f6 100644
--- a/algebra/ring.hlean
+++ b/algebra/ring.hlean
@@ -5,14 +5,22 @@ import algebra.ring .direct_sum ..heq ..move_to_lib
 open algebra group eq is_trunc sigma
 
 namespace algebra
-definition AbGroup_of_Ring [constructor] (R : Ring) : AbGroup :=
-AbGroup.mk R (add_ab_group_of_ring R)
+definition AddAbGroup_of_Ring [constructor] (R : Ring) : AddAbGroup :=
+AddAbGroup.mk R (add_ab_group_of_ring R)
 
-definition ring_AbGroup_of_Ring [instance] (R : Ring) : ring (AbGroup_of_Ring R) :=
+definition AddGroup_of_Ring [constructor] (R : Ring) : AddGroup :=
+AddGroup.mk R (add_group_of_add_ab_group R)
+
+definition ring_AddAbGroup_of_Ring [instance] (R : Ring) : ring (AddAbGroup_of_Ring R) :=
 Ring.struct R
 
+/- we give the following instance very high priority, otherwise type class inference would sometimes find the additive structure of R as the group structure. -/
+definition monoid_AddAbGroup_of_Ring [instance] [priority 3000] [constructor] (R : Ring) :
+  monoid (Group_of_AbGroup (AddAbGroup_of_Ring R)) :=
+@monoid_of_ring _ (Ring.struct R)
+
 definition ring_right_action [constructor] {R : Ring} (r : R) :
-  AbGroup_of_Ring R →g AbGroup_of_Ring R :=
+  AddAbGroup_of_Ring R →a AddAbGroup_of_Ring R :=
 homomorphism.mk (λs, s * r) (λs s', !right_distrib)
 
 definition ring_of_ab_group [constructor] (G : Type) [ab_group G] (m : G → G → G) (o : G)
diff --git a/algebra/spectral_sequence.hlean b/algebra/spectral_sequence.hlean
index 9a33df5..cc0dda3 100644
--- a/algebra/spectral_sequence.hlean
+++ b/algebra/spectral_sequence.hlean
@@ -36,7 +36,7 @@ convergent_spectral_sequence (λn s, LeftModule_int_of_AbGroup (E' n s))
 
   definition convergent_spectral_sequence_of_exact_couple {R : Ring} {E' : agℤ → agℤ → LeftModule R}
     {Dinf : agℤ → LeftModule R} (c : convergent_exact_couple E' Dinf)
-    (st_eq : Πn, (st c n).1 + (st c n).2 = n) (deg_i_eq : deg (i (X c)) 0 = (-(1 : ℤ), (1 : ℤ))) :
+    (st_eq : Πn, (st c n).1 + (st c n).2 = n) (deg_i_eq : deg (i (X c)) 0 = (- 1, 1)) :
     convergent_spectral_sequence E' Dinf :=
   convergent_spectral_sequence.mk (λr, E (page (X c) r)) (λr, d (page (X c) r))
     (deg_d c) (deg_d_eq0 c)
@@ -49,8 +49,8 @@ convergent_spectral_sequence (λn s, LeftModule_int_of_AbGroup (E' n s))
       induction p with p IH,
       { exact !prod.eta⁻¹ ⬝ prod_eq (eq_sub_of_add_eq (ap (add _) !zero_add ⬝ st_eq n))
                                     (zero_add (st c n).2)⁻¹ },
-      { assert H1 : Π(a : ℤ), n - (p + a) - (1 : ℤ) = n - (succ p + a),
-        exact λa, !sub_add_eq_sub_sub⁻¹ ⬝ ap (sub n) (add_comm_middle p a (1 : ℤ) ⬝ proof idp qed),
+      { assert H1 : Π(a : ℤ), n - (p + a) - 1 = n - (succ p + a),
+        exact λa, !sub_add_eq_sub_sub⁻¹ ⬝ ap (sub n) (add_comm_middle p a 1 ⬝ proof idp qed),
         assert H2 : Π(a : ℤ), p + a + 1 = succ p + a,
         exact λa, add_comm_middle p a 1,
         refine ap (deg (i (X c))) IH ⬝ !deg_eq ⬝ ap (add _) deg_i_eq ⬝ prod_eq !H1 !H2 }
diff --git a/cohomology/serre.hlean b/cohomology/serre.hlean
index 6059149..e6c6ab4 100644
--- a/cohomology/serre.hlean
+++ b/cohomology/serre.hlean
@@ -232,6 +232,22 @@ section atiyah_hirzebruch
     { reflexivity }
   end
 
+/-
+  to unfold a field of atiyah_hirzebruch_spectral_sequence:
+    esimp [atiyah_hirzebruch_spectral_sequence, convergent_spectral_sequence_of_exact_couple,
+      atiyah_hirzebruch_convergence, convergent_exact_couple_g_isomorphism,
+      convergent_exact_couple_isomorphism, convergent_exact_couple_reindex,
+      atiyah_hirzebruch_convergence2, convergent_exact_couple_negate_abutment,
+      atiyah_hirzebruch_convergence1, convergent_exact_couple_sequence],
+
+-/
+  definition AHSS_deg_d (r : ℕ) :
+    convergent_spectral_sequence.deg_d atiyah_hirzebruch_spectral_sequence r =
+    (r + 2, -(r + 1)) :=
+  begin
+    reflexivity
+  end
+
 end atiyah_hirzebruch
 
 section unreduced_atiyah_hirzebruch
diff --git a/homotopy/EMRing.hlean b/homotopy/EMRing.hlean
index 9093f1c..b85a7d4 100644
--- a/homotopy/EMRing.hlean
+++ b/homotopy/EMRing.hlean
@@ -8,10 +8,10 @@ namespace EM
 
 
 definition EM1product_adj {R : Ring} :
-  EM1 (AbGroup_of_Ring R) →* ppmap (EM1 (AbGroup_of_Ring R)) (EMadd1 (AbGroup_of_Ring R) 1) :=
+  EM1 (AddGroup_of_Ring R) →* ppmap (EM1 (AddGroup_of_Ring R)) (EMadd1 (AddAbGroup_of_Ring R) 1) :=
 begin
-  have is_trunc 1 (ppmap (EM1 (AbGroup_of_Ring R)) (EMadd1 (AbGroup_of_Ring R) 1)),
-    from is_trunc_pmap_of_is_conn _ _ _ _ _ _ (le.refl 2) !is_trunc_EMadd1,
+  have is_trunc 1 (ppmap (EM1 (AddGroup_of_Ring R)) (EMadd1 (AddAbGroup_of_Ring R) 1)),
+    from is_trunc_pmap_of_is_conn _ _ !is_conn_EM1 _ _ _ (le.refl 2) !is_trunc_EMadd1,
   apply EM1_pmap, fapply inf_homomorphism.mk,
   { intro r, refine pfunext _ _, exact !loop_EM2⁻¹ᵉ* ∘* EM1_functor (ring_right_action r), },
   { intro r r', exact sorry }