fix(hott): adjust library to new apply tactic semantics

hott/algebra/category/basic.hlean

@@ -25,6 +25,8 @@ namespace category
   definition path_of_iso {a b : ob} : a ≅ b → a = b :=
   iso_of_path⁻¹
 
+  set_option apply.class_instance false -- disable class instance resolution in the apply tactic
+
   definition ob_1_type : is_trunc nat.zero .+1 ob :=
   begin
     apply is_trunc_succ, intros (a, b),

hott/algebra/precategory/constructions.hlean

@@ -28,6 +28,8 @@ namespace precategory
 
   variables {C : Precategory} {a b c : C}
 
+  set_option apply.class_instance false -- disable class instance resolution in the apply tactic
+
   theorem compose_op {f : hom a b} {g : hom b c} : f ∘op g = g ∘ f := idp
 
   -- TODO: Decide whether just to use funext for this theorem or

hott/algebra/precategory/functor.hlean

@@ -44,6 +44,8 @@ namespace functor
     apply (prod.rec_on P1), intros (d3, d4), apply idp,
   end
 
+  set_option apply.class_instance false -- disable class instance resolution in the apply tactic
+
   protected definition strict_cat_has_functor_hset
     [HD : is_hset (objects D)] : is_hset (functor C D) :=
   begin

hott/algebra/precategory/iso.hlean

@@ -40,6 +40,8 @@ namespace morphism
     intro S, apply (sigma.rec_on S), intros (f, H), apply idp,
   end
 
+  set_option apply.class_instance false -- disable class instance resolution in the apply tactic
+
   -- The statement "f is an isomorphism" is a mere proposition
   definition is_hprop_of_is_iso : is_hset (is_iso f) :=
   begin

hott/algebra/precategory/natural_transformation.hlean

@@ -26,11 +26,11 @@ namespace natural_transformation
     (λ a, η a ∘ θ a)
     (λ a b f,
       calc
-	H f ∘ (η a ∘ θ a) = (H f ∘ η a) ∘ θ a : assoc
-		      ... = (η b ∘ G f) ∘ θ a : naturality η f
-		      ... = η b ∘ (G f ∘ θ a) : assoc
-		      ... = η b ∘ (θ b ∘ F f) : naturality θ f
-		      ... = (η b ∘ θ b) ∘ F f : assoc)
+        H f ∘ (η a ∘ θ a) = (H f ∘ η a) ∘ θ a : assoc
+                      ... = (η b ∘ G f) ∘ θ a : naturality η f
+                      ... = η b ∘ (G f ∘ θ a) : assoc
+                      ... = η b ∘ (θ b ∘ F f) : naturality θ f
+                      ... = (η b ∘ θ b) ∘ F f : assoc)
 
   infixr `∘n`:60 := compose
 
@@ -47,6 +47,7 @@ namespace natural_transformation
     apply (dcongr_arg2 (@natural_transformation.mk C D F G) p₁ p₂),
   end
 
+  set_option apply.class_instance false -- disable class instance resolution in the apply tactic
 
   protected definition assoc (η₃ : H ⟹ I) (η₂ : G ⟹ H) (η₁ : F ⟹ G) :
       η₃ ∘n (η₂ ∘n η₁) = (η₃ ∘n η₂) ∘n η₁ :=

hott/trunc.hlean

@@ -28,9 +28,9 @@ namespace truncation
     (Π (x y : A), is_trunc n (x = y)) ≃ (is_trunc (n .+1) A) :=
   begin
     fapply equiv.mk,
-      intro H, apply is_trunc_succ, exact H,
+      intro H, apply is_trunc_succ,
     fapply is_equiv.adjointify,
-        intros (H, x, y), apply succ_is_trunc, exact H,
+        intros (H, x, y), apply succ_is_trunc,
       intro H, apply (is_trunc.rec_on H), intro Hint, apply idp,
     intro P,
    exact sorry,
@@ -56,9 +56,6 @@ namespace truncation
     apply trunc_equiv,
       apply equiv.to_is_equiv,
       apply is_trunc.pi_char,
-    apply trunc_pi, intro a,
-    apply trunc_pi, intro b,
-    apply (IH (a = b)),
   end
 
 end truncation

hott/types/pi.hlean

@@ -99,7 +99,7 @@ namespace pi
     apply (trunc_index.rec_on n),
       intros (B, H),
         fapply is_contr.mk,
-          intro a, apply center, apply H, --remove "apply H" when term synthesis works correctly
+          intro a, apply center,
           intro f, apply path_pi,
             intro x, apply (contr (f x)),
       intros (n, IH, B, H),
@@ -116,8 +116,7 @@ namespace pi
       [H : ∀a, is_trunc n (f a = g a)] : is_trunc n (f = g) :=
   begin
     apply trunc_equiv', apply equiv.symm,
-    apply path_equiv_homotopy,
-    apply trunc_pi, exact H,
+    apply path_equiv_homotopy
   end
 
 end pi

hott/types/sigma.hlean

@@ -451,14 +451,13 @@ namespace sigma
     intros (A, B, HA, HB),
       fapply trunc_equiv',
         apply equiv.symm,
-          apply equiv_center_of_contr, apply HA, --should be solved by term synthesis
-        apply HB,
+          apply equiv_center_of_contr,
      intros (n, IH, A, B, HA, HB),
        fapply is_trunc_succ, intros (u, v),
       fapply trunc_equiv',
          apply equiv_sigma_path,
          apply IH,
-           apply succ_is_trunc, assumption,
+           apply succ_is_trunc,
            intro p,
              show is_trunc n (p ▹ u .2 = v .2), from
              succ_is_trunc n (p ▹ u.2) (v.2),