fix(tests/lean/run): adjust some tests to changes in the standard library

tests/lean/run/252.lean

@@ -6,7 +6,7 @@ node : tree A → tree A → tree A
 
 check tree.node
 
-definition size {A : Type} (t : tree A) :=
+definition size {A : Type} (t : tree A) : nat :=
 tree.rec (λ a, 1) (λ t₁ t₂ n₁ n₂, n₁ + n₂) t
 
 check size

tests/lean/run/331.lean

@@ -9,7 +9,7 @@ open nat
 check less.rec_on
 
 namespace foo1
-protected definition foo2.bar := 10
+protected definition foo2.bar : nat := 10
 end foo1
 
 example : foo1.foo2.bar = 10 :=

tests/lean/run/505.lean

@@ -1,5 +1,5 @@
 import data.set
-open set
+open set nat
 
 section
   variable {A : Type}
@@ -13,8 +13,8 @@ section
   notation `⦃` s:(foldr `,` (a t, insert a t) ∅) `⦄` := s
   notation `{` `{` s:(foldr `,` (a t, insert a t) ∅) `}` `}` := s
 
-  check ⦃1, 2, 3⦄
-  check {{1, 2, 3}}
+  check ⦃(1:nat), 2, 3⦄
+  check {{(1:nat), 2, 3}}
 
   definition foo  {X : Type} {{ x : X }} : X := x
 end

tests/lean/run/511a.lean

@@ -5,7 +5,7 @@ example (a b : nat) (f : nat → nat) (h : f (succ a) = 0) : f (a+1) = 0 :=
 by rewrite [add_one, h]
 
 example (a b : nat) (f : nat → nat) (h : f (succ a) = 0) : f (a+1) = 0 :=
-by xrewrite h
+by krewrite h
 
 definition g (a : nat) := a + 1
 definition h (a : nat) := a

tests/lean/run/568.lean

@@ -1,15 +1,15 @@
 namespace f1
-  definition flip := 20
+  definition flip := (20:num)
 end f1
 
 namespace f2
-  definition flip := 10
+  definition flip := (10:num)
 end f2
 
 namespace f3
   export [declarations] f1
-  export -[declarations] f2
+  export - [declarations] f2
 end f3
 
 export [declarations] f1
-export -[declarations] f2
+export - [declarations] f2

tests/lean/run/668.lean

@@ -4,7 +4,7 @@ namespace Nat
   constant Nat : Type₁
   constant num2Nat : num → Nat
   attribute num2Nat [coercion]
-  check (0 : Nat)
+  definition foo : Nat := (0:num)
 end Nat
 
 constant Int : Type₁
@@ -13,8 +13,8 @@ namespace Int
   open Nat
   constant Nat2Int : Nat → Int
   attribute Nat2Int [coercion]
-  check (0 : Int)
+  definition foo : Int := (0:num)
 end Int
 
 open Int
-check (0 : Int)
+definition foo : Int := (0:num)

tests/lean/run/695e.lean

@@ -1,3 +1,4 @@
+import data.nat
 open nat
 example (n : ℕ) : n + 1 = succ n :=
-by rewrite [<d n+1]
+by rewrite [-add_one]

tests/lean/run/791.lean

@@ -1,5 +1,6 @@
-definition foo.bar := 10
-definition boo.bla.foo := 20
+open nat
+definition foo.bar : nat := 10
+definition boo.bla.foo : nat := 20
 
 open foo
 open boo.bla

tests/lean/run/801.lean

@@ -3,7 +3,7 @@ definition seq_diagram (A : ℕ → Type) : Type := (Πn, A n → A (succ n))
 variables (A : ℕ → Type) (f : seq_diagram A)
 include f
 
-definition shift_diag [unfold-full] (k : ℕ) : seq_diagram (λn, A (k + n)) :=
+definition shift_diag [unfold_full] (k : ℕ) : seq_diagram (λn, A (k + n)) :=
 λn a, f (k + n) a
 
 example (n k : ℕ) (b : A (k + n)) : shift_diag A f k n b = sorry :=

tests/lean/run/809.lean

@@ -3,7 +3,7 @@ open finset num nat int algebra
 
 check @finset.insert _ _ 1 (@finset.empty ℕ)
 
-check '{1, 2, 3}               -- finset num
+check '{(1:nat), 2, 3}
 check ('{1, 2, 3} : finset ℕ)
 check ('{1, 2, 3} : finset ℕ)  -- finset ℕ
 check ('{1, 2, 3} : finset ℤ)  -- finset ℤ

tests/lean/run/alg_rw.lean

@@ -10,14 +10,11 @@ section
   mul_one 1
 end
 
-definition one [reducible] (A : Type) [s : has_one A] : A :=
-!has_one.one
-
 section
   variable {A : Type}
   variable [s : comm_group A]
   include s
 
-  theorem one_mul_one2 : (one A) * 1 = 1 :=
+  theorem one_mul_one2 : (one : A) * 1 = 1 :=
   by rewrite one_mul_one
 end

tests/lean/run/algebra3.lean

@@ -1,14 +1,5 @@
 import logic
 
-structure has_mul [class] (A : Type) :=
-(mul : A → A → A)
-
-structure has_one [class] (A : Type) :=
-(one : A)
-
-structure has_inv [class] (A : Type) :=
-(inv : A → A)
-
 infixl `*`   := has_mul.mul
 postfix `⁻¹` := has_inv.inv
 notation 1   := has_one.one

tests/lean/run/all_goals.lean

@@ -7,6 +7,5 @@ attribute nat.rec_on [unfold 2]
 example (a b c : nat) : a + 0 = 0 + a ∧ b + 0 = 0 + b :=
 begin
   apply and.intro,
-  all_goals esimp[of_num],
   all_goals (state; rewrite zero_add)
 end

tests/lean/run/all_goals2.lean

@@ -18,6 +18,6 @@ example (a b c : nat) : (a + 0 = 0 + a ∧ b + 0 = 0 + b) ∧ c = c :=
 
 begin
   apply and.intro,
-  apply and.intro ;; (esimp[of_num]; state; rewrite zero_add),
+  apply and.intro ;; (state; rewrite zero_add),
   apply rfl
 end

tests/lean/run/app_builder.lean

@@ -1,4 +1,4 @@
-definition a := 10
+definition a :num := 10
 
 constant b : num
 constant c : num

tests/lean/run/assert_tac2.lean

@@ -1,5 +1,5 @@
 import data.nat
-open nat eq.ops
+open nat eq.ops algebra
 
 theorem lcm_dvd {m n k : nat} (H1 : m ∣ k) (H2 : (n ∣ k)) : (lcm m n ∣ k) :=
 match eq_zero_or_pos k with

tests/lean/run/atomic_notation.lean

@@ -1,6 +1,6 @@
 import logic data.num
 open num
 constant f : num → num
-notation `o`:1 := 10
+notation `o`:1 := (10:num)
 check o + 1
 check f o + o + o

tests/lean/run/bquant.lean

@@ -1,11 +1,11 @@
 import data.nat.bquant
 open nat
 
-example : is_true (∀ x, x ≤ 4 → x ≠ 6) :=
+example : is_true (∀ x : nat, x ≤ 4 → x ≠ 6) :=
 trivial
 
-example : is_false (∀ x, x ≤ 5 → ∀ y, y < x → y * y ≠ x) :=
+example : is_false (∀ x : nat, x ≤ 5 → ∀ y, y < x → y * y ≠ x) :=
 trivial
 
-example : is_true (∀ x, x < 5 → ∃ y, y ≤ x + 5 ∧ y = 2*x) :=
+example : is_true (∀ x : nat, x < 5 → ∃ y, y ≤ x + 5 ∧ y = 2*x) :=
 trivial

tests/lean/run/choose_test.lean

@@ -1,7 +1,7 @@
 import data.encodable
 open nat encodable
 
-theorem ex : ∃ x, x > 3 :=
+theorem ex : ∃ x : nat, x > 3 :=
 exists.intro 6 dec_trivial
 
 reveal ex

tests/lean/run/class5.lean

@@ -44,7 +44,7 @@ section
   -- check mul_struct nat  << This is an error, we opened only the notation from algebra
   variables a b c : nat
   check a*b*c
-  definition tst3 : nat := #nat a*b*c
+  definition tst3 : nat := a*b*c
 end
 
 section

tests/lean/run/class_coe.lean

@@ -40,12 +40,6 @@ check x + i
 check n + x
 check x + n
 check x + i + n
-check n + 0
-check 0 + n
-check 0 + i
-check i + 0
-check 0 + x
-check x + 0
 namespace foo
 constant eq {A : Type} : A → A → Prop
 infixl `=` := eq

tests/lean/run/constr_tac.lean

@@ -45,7 +45,7 @@ end
 
 open nat
 
-example (a : nat) : a > 0 → ∃ x, x > 0 :=
+example (a : nat) : a > 0 → ∃ x : nat, x > 0 :=
 begin
   intro Ha,
   existsi a,

tests/lean/run/contra1.lean

@@ -1,10 +1,12 @@
+open nat
+
 example (a b : nat) (h : false) : a = b :=
 by contradiction
 
 example : ∀ (a b : nat), false → a = b :=
 by contradiction
 
-example : ∀ (a b : nat), 0 = 1 → a = b :=
+example : ∀ (a b : nat), (0:nat) = 1 → a = b :=
 by contradiction
 
 definition id {A : Type} (a : A) := a
@@ -12,5 +14,5 @@ definition id {A : Type} (a : A) := a
 example : ∀ (a b : nat), id false → a = b :=
 by contradiction
 
-example : ∀ (a b : nat), id (0 = 1) → a = b :=
+example : ∀ (a b : nat), id ((0:nat) = 1) → a = b :=
 by contradiction

tests/lean/run/diag.lean

@@ -11,7 +11,7 @@ nat.rec_on n
     let t₁ : vector (vector A n₁) n₁ := map tail (tail v) in
     h₁ :: r t₁)
 
-example : diag ((1 :: 2 :: 3 :: nil) :: (4 :: 5 :: 6 :: nil) :: (7 :: 8 :: 9 :: nil) :: nil) = 1 :: 5 :: 9 :: nil :=
+example : diag ((1 :: 2 :: 3 :: nil) :: (4 :: 5 :: 6 :: nil) :: (7 :: 8 :: 9 :: nil) :: nil) = (1 :: 5 :: 9 :: nil : vector num 3)  :=
 rfl
 
 end vector

tests/lean/run/div_wf.lean

@@ -26,7 +26,7 @@ rfl
 -- The actual definitional package would not do that.
 -- It will always pack things.
 
-definition pair_nat.lt    := lex lt lt  -- Could also be (lex lt empty_rel)
+definition pair_nat.lt    := lex nat.lt nat.lt  -- Could also be (lex lt empty_rel)
 definition pair_nat.lt.wf [instance] : well_founded pair_nat.lt :=
 prod.lex.wf lt.wf lt.wf
 infixl `≺`:50 := pair_nat.lt

tests/lean/run/eq15.lean

@@ -13,5 +13,5 @@ rfl
 theorem append_cons {A : Type} (h : A) (t l : list A) : append (h :: t) l = h :: (append t l) :=
 rfl
 
-example : append (1 :: 2 :: nil) (3 :: 4 :: 5 :: nil) = (1 :: 2 :: 3 :: 4 :: 5 :: nil) :=
+example : append ((1:nat) :: 2 :: nil) (3 :: 4 :: 5 :: nil) = (1 :: 2 :: 3 :: 4 :: 5 :: nil) :=
 rfl

tests/lean/run/eq16.lean

@@ -14,5 +14,5 @@ rfl
 theorem append_cons (h : A) (t l : list A) : append (h :: t) l = h :: (append t l) :=
 rfl
 
-example : append (1 :: 2 :: nil) (3 :: 4 :: 5 :: nil) = (1 :: 2 :: 3 :: 4 :: 5 :: nil) :=
+example : append ((1:num) :: 2 :: nil) (3 :: 4 :: 5 :: nil) = (1 :: 2 :: 3 :: 4 :: 5 :: nil) :=
 rfl

tests/lean/run/eq25.lean

@@ -6,6 +6,6 @@ definition Nat := N
 
 open N
 
-definition add : Nat → Nat → Nat
-| add O     b := b
-| add (S a) b := S (add a b)
+definition add1 : Nat → Nat → Nat
+| add1 O     b := b
+| add1 (S a) b := S (add1 a b)

tests/lean/run/eq6.lean

@@ -11,5 +11,5 @@ rfl
 theorem append_cons {A : Type} (h : A) (t l : list A) : append (h :: t) l = h :: (append t l) :=
 rfl
 
-example : append (1 :: 2 :: nil) (3 :: 4 :: 5 :: nil) = (1 :: 2 :: 3 :: 4 :: 5 :: nil) :=
+example : append ((1:nat) :: 2 :: nil) (3 :: 4 :: 5 :: nil) = (1 :: 2 :: 3 :: 4 :: 5 :: nil) :=
 rfl

tests/lean/run/ex.lean

@@ -1,3 +1,4 @@
 import standard
 set_option pp.implicit true
-check ∃x, x = 0
+check ∃x, x = (0:num)
+check ∃x:num, x = 0

tests/lean/run/export2.lean

@@ -1,6 +1,6 @@
 open nat
 
-definition foo := 30
+definition foo : nat := 30
 
 namespace foo
   definition x : nat := 10

tests/lean/run/fib_brec.lean

@@ -19,9 +19,9 @@ namespace nat
   definition fib (n : nat) :=
   nat.brec_on n (λ (n : nat),
     nat.cases_on n
-      (λ (b₀ : nat.below zero), succ zero)
+      (λ (b₀ : nat.below 0), succ 0)
       (λ (n₁ : nat), nat.cases_on n₁
-          (λ b₁ : nat.below (succ zero), succ zero)
+          (λ b₁ : nat.below (succ 0), succ zero)
           (λ (n₂ : nat) (b₂ : nat.below (succ (succ n₂))), pr₁ b₂ + pr₁ (pr₂ b₂))))
 
   theorem fib_0 : fib 0 = 1 :=

tests/lean/run/finset.lean

@@ -167,7 +167,7 @@ namespace finset
   theorem empty_union {A : Type} (s : finset A) : ∅ ∪ s = s :=
   quot.induction_on s (λ l, quot.sound (λ a, by rewrite append_nil_left))
 
-  example : to_finset (1::2::nil) ∪ to_finset (2::3::nil) = ⟦1 :: 2 :: 2 :: 3 :: nil⟧ :=
+  example : to_finset ((1:nat)::2::nil) ∪ to_finset (2::3::nil) = ⟦1 :: 2 :: 2 :: 3 :: nil⟧ :=
   rfl
 
   example : to_finset [(1:nat), 1, 2, 3] = to_finset [2, 3, 1, 2, 2, 3] :=

tests/lean/run/forest_height.lean

@@ -1,5 +1,5 @@
 import data.nat data.sum data.sigma data.bool
-open nat sigma
+open nat sigma algebra
 
 inductive tree (A : Type) : Type :=
 | node : A → forest A → tree A

tests/lean/run/gcd.lean

@@ -4,7 +4,7 @@ open nat well_founded decidable prod eq.ops
 namespace playground
 
 -- Setup
-definition pair_nat.lt    := lex lt lt
+definition pair_nat.lt    := lex nat.lt nat.lt
 definition pair_nat.lt.wf [instance] : well_founded pair_nat.lt :=
 intro_k (prod.lex.wf lt.wf lt.wf) 20 -- the '20' is for being able to execute the examples... it means 20 recursive call without proof computation
 infixl `≺`:50 := pair_nat.lt

tests/lean/run/group.lean

@@ -26,10 +26,10 @@ definition group_to_struct [instance] (g : group) : group_struct (carrier g)
 
 check group_struct
 
-definition mul {A : Type} {s : group_struct A} (a b : A) : A
+definition mul1 {A : Type} {s : group_struct A} (a b : A) : A
 := group_struct.rec (λ mul one inv h1 h2 h3, mul) s a b
 
-infixl `*` := mul
+infixl `*` := mul1
 
 constant  G1 : group.{1}
 constant  G2 : group.{1}

tests/lean/run/group2.lean

@@ -28,10 +28,10 @@ definition group_to_struct [instance] (g : group) : group_struct (carrier g)
 
 check group_struct
 
-definition mul {A : Type} [s : group_struct A] (a b : A) : A
+definition mul1 {A : Type} [s : group_struct A] (a b : A) : A
 := group_struct.rec (λ mul one inv h1 h2 h3, mul) s a b
 
-infixl `*` := mul
+infixl `*` := mul1
 
 section
   variable  G1 : group

tests/lean/run/imp2.lean

@@ -1,4 +1,4 @@
 import data.num
-check (λ {A : Type.{1}} (a : A), a) 10
+check (λ {A : Type.{1}} (a : A), a) (10:num)
 check (λ {A} a, a) 10
-check (λ a, a) 10
+check (λ a, a) (10:num)

tests/lean/run/interp.lean

@@ -8,7 +8,7 @@ inductive univ :=
 
 open univ
 
-definition interp : univ → Type₁
+definition interp [reducible] : univ → Type₁
 | ubool          := bool
 | unat           := nat
 | (uarrow fr to) := interp fr → interp to
@@ -23,7 +23,7 @@ definition is_even : nat → bool
 | zero     := tt
 | (succ n) := bnot (is_even n)
 
-example : foo unat 10  = 11 := rfl
+example : foo unat (10:nat)  = 11 := rfl
 example : foo ubool tt = ff := rfl
 example : foo (uarrow unat ubool) (λ x : nat, is_even x) 3 = tt := rfl
 example : foo (uarrow unat ubool) (λ x : nat, is_even x) 4 = ff := rfl

tests/lean/run/is_true.lean

@@ -1,8 +1,8 @@
 import data.nat
 open nat
 
-example : is_true (2 = 2)  := trivial
-example : is_false (3 = 2) := trivial
-example : is_true (2 < 3) := trivial
-example : is_true (3 ∣ 9) := trivial
-example : is_false (3 ∣ 7) := trivial
+example : is_true (2 = (2:nat))  := trivial
+example : is_false (3 = (2:nat)) := trivial
+example : is_true (2 < (3:nat)) := trivial
+example : is_true (3 ∣ (9:nat)) := trivial
+example : is_false (3 ∣ (7:nat)) := trivial

tests/lean/run/issue332.lean

@@ -7,5 +7,5 @@ intro a, exact a
 end
 check @foo
 
-example : foo 10 = 10 :=
+example : foo 10 = (10:num) :=
 rfl

tests/lean/run/let_tac.lean

@@ -1,4 +1,5 @@
 import data.nat
+open algebra
 
 example (a b : Prop) : a → b → a ∧ b :=
 begin

tests/lean/run/localcoe.lean

@@ -12,5 +12,6 @@ section
 
   local attribute foo [coercion]
 
-  check s 10
+  check let a : nat := 10 in s a
+
 end

tests/lean/run/matrix.lean

@@ -2,18 +2,18 @@ import logic
 
 constant matrix.{l} : Type.{l} → Type.{l}
 constant same_dim {A : Type} : matrix A → matrix A → Prop
-constant add {A : Type} (m1 m2 : matrix A) {H : same_dim m1 m2} : matrix A
+constant add1 {A : Type} (m1 m2 : matrix A) {H : same_dim m1 m2} : matrix A
 
-theorem same_dim_irrel {A : Type} {m1 m2 : matrix A} {H1 H2 : same_dim m1 m2} : @add A m1 m2 H1 = @add A m1 m2 H2 :=
+theorem same_dim_irrel {A : Type} {m1 m2 : matrix A} {H1 H2 : same_dim m1 m2} : @add1 A m1 m2 H1 = @add1 A m1 m2 H2 :=
 rfl
 open eq
 theorem same_dim_eq_args {A : Type} {m1 m2 m1' m2' : matrix A} (H1 : m1 = m1') (H2 : m2 = m2') (H : same_dim m1 m2) : same_dim m1' m2' :=
 subst H1 (subst H2 H)
 
-theorem add_congr {A : Type} (m1 m2 m1' m2' : matrix A) (H1 : m1 = m1') (H2 : m2 = m2') (H : same_dim m1 m2) : @add A m1 m2 H = @add A m1' m2' (same_dim_eq_args H1 H2 H) :=
-have base : ∀ (H1 : m1 = m1) (H2 : m2 = m2), @add A m1 m2 H = @add A m1 m2 (eq.rec (eq.rec H H1) H2), from
+theorem add1_congr {A : Type} (m1 m2 m1' m2' : matrix A) (H1 : m1 = m1') (H2 : m2 = m2') (H : same_dim m1 m2) : @add1 A m1 m2 H = @add1 A m1' m2' (same_dim_eq_args H1 H2 H) :=
+have base : ∀ (H1 : m1 = m1) (H2 : m2 = m2), @add1 A m1 m2 H = @add1 A m1 m2 (eq.rec (eq.rec H H1) H2), from
   assume H1 H2, rfl,
-have general : ∀ (H1 : m1 = m1') (H2 : m2 = m2'), @add A m1 m2 H = @add A m1' m2' (eq.rec (eq.rec H H1) H2), from
+have general : ∀ (H1 : m1 = m1') (H2 : m2 = m2'), @add1 A m1 m2 H = @add1 A m1' m2' (eq.rec (eq.rec H H1) H2), from
   subst H1 (subst H2 base),
-calc @add A m1 m2 H = @add A m1' m2' (eq.rec (eq.rec H H1) H2)  : general H1 H2
-            ...     = @add A m1' m2' (same_dim_eq_args H1 H2 H) : same_dim_irrel
+calc @add1 A m1 m2 H = @add1 A m1' m2' (eq.rec (eq.rec H H1) H2)  : general H1 H2
+            ...     = @add1 A m1' m2' (same_dim_eq_args H1 H2 H) : same_dim_irrel

tests/lean/run/matrix2.lean

@@ -2,14 +2,14 @@ import logic
 
 constant matrix.{l} : Type.{l} → Type.{l}
 constant same_dim {A : Type} : matrix A → matrix A → Prop
-constant add {A : Type} (m1 m2 : matrix A) {H : same_dim m1 m2} : matrix A
+constant add1 {A : Type} (m1 m2 : matrix A) {H : same_dim m1 m2} : matrix A
 open eq
 theorem same_dim_eq_args {A : Type} {m1 m2 m1' m2' : matrix A} (H1 : m1 = m1') (H2 : m2 = m2') (H : same_dim m1 m2) : same_dim m1' m2' :=
 subst H1 (subst H2 H)
 
-theorem add_congr {A : Type} (m1 m2 m1' m2' : matrix A) (H1 : m1 = m1') (H2 : m2 = m2') (H : same_dim m1 m2) : @add A m1 m2 H = @add A m1' m2' (same_dim_eq_args H1 H2 H) :=
-have base : ∀ (H1 : m1 = m1) (H2 : m2 = m2), @add A m1 m2 H = @add A m1 m2 (eq.rec (eq.rec H H1) H2), from
+theorem add1_congr {A : Type} (m1 m2 m1' m2' : matrix A) (H1 : m1 = m1') (H2 : m2 = m2') (H : same_dim m1 m2) : @add1 A m1 m2 H = @add1 A m1' m2' (same_dim_eq_args H1 H2 H) :=
+have base : ∀ (H1 : m1 = m1) (H2 : m2 = m2), @add1 A m1 m2 H = @add1 A m1 m2 (eq.rec (eq.rec H H1) H2), from
   assume H1 H2, rfl,
-have general : ∀ (H1 : m1 = m1') (H2 : m2 = m2'), @add A m1 m2 H = @add A m1' m2' (eq.rec (eq.rec H H1) H2), from
+have general : ∀ (H1 : m1 = m1') (H2 : m2 = m2'), @add1 A m1 m2 H = @add1 A m1' m2' (eq.rec (eq.rec H H1) H2), from
   subst H1 (subst H2 base),
 general H1 H2

tests/lean/run/measurable.lean

@@ -3,5 +3,5 @@ open prod nat
 example (a b : nat) : size_of (a, true, bool.tt, (λ c d : nat, c + d), option.some b) = a + b :=
 rfl
 
-example : size_of (pair (pair (pair 2 true) (λ a : nat, a)) (option.some 3)) = 5 :=
+example : size_of (pair (pair (pair (2:nat) true) (λ a : nat, a)) (option.some (3:nat))) = 5 :=
 rfl

tests/lean/run/nat_bug2.lean

@@ -20,7 +20,7 @@ axiom add_one (n:nat) : n + (succ zero) = succ n
 axiom add_le_right {n m : nat} (H : n ≤ m) (k : nat) : n + k ≤ m + k
 
 theorem succ_le {n m : nat} (H : n ≤ m) : succ n ≤ succ m
-:= add_one m ▸ add_one n ▸ add_le_right H 1
+:= add_one m ▸ add_one n ▸ add_le_right H (1:num)
 
 end nat
 end experiment

tests/lean/run/nested_rec.lean

@@ -34,7 +34,7 @@ calc g (succ a) = pr₁ (well_founded.fix g.F (succ a)) : rfl
 theorem g_all_zero (a : nat) : g a = zero :=
 nat.induction_on a
   g_zero
-  (λ a₁ (ih : g a₁ = zero), calc
+  (λ a₁ (ih : g a₁ = 0), calc
      g (succ a₁) = g (g a₁) : g_succ
           ...    = g 0      : ih
           ...    = 0        : g_zero)

tests/lean/run/new_obtains.lean

@@ -63,14 +63,4 @@ exists.intro
   (x+y)
   (calc a+b = 2*x + 2*y : by rewrite [Hx, Hy]
         ... = 2*(x+y)   : by rewrite mul.left_distrib)
-
-theorem dvd_of_dvd_add_left {m n₁ n₂ : ℕ} (H₁ : m ∣ n₁ + n₂) (H₂ : m ∣ n₁) : m ∣ n₂ :=
-obtain (c₁ : nat) (Hc₁ : n₁ + n₂ = m * c₁), from H₁,
-obtain (c₂ : nat) (Hc₂ : n₁ = m * c₂), from H₂,
-have   aux : m * (c₁ - c₂) = n₂, from calc
-  m * (c₁ - c₂) = m * c₁  - m * c₂ : by rewrite mul_sub_left_distrib
-           ...  = n₁ + n₂ - m * c₂ : Hc₁
-           ...  = n₁ + n₂ - n₁     : Hc₂
-           ...  = n₂               : add_sub_cancel_left,
-dvd.intro aux
 end hidden

tests/lean/run/num_sub.lean

@@ -1,83 +1,83 @@
 open num bool
 
-example : le 0 0 = tt := rfl
-example : le 0 1 = tt := rfl
-example : le 0 2 = tt := rfl
-example : le 0 3 = tt := rfl
+example : num.le 0 0 = tt := rfl
+example : num.le 0 1 = tt := rfl
+example : num.le 0 2 = tt := rfl
+example : num.le 0 3 = tt := rfl
 
-example : le 1 0 = ff := rfl
-example : le 1 1 = tt := rfl
-example : le 1 2 = tt := rfl
-example : le 1 3 = tt := rfl
+example : num.le 1 0 = ff := rfl
+example : num.le 1 1 = tt := rfl
+example : num.le 1 2 = tt := rfl
+example : num.le 1 3 = tt := rfl
 
-example : le 2 0 = ff := rfl
-example : le 2 1 = ff := rfl
-example : le 2 2 = tt := rfl
-example : le 2 3 = tt := rfl
-example : le 2 4 = tt := rfl
-example : le 2 5 = tt := rfl
+example : num.le 2 0 = ff := rfl
+example : num.le 2 1 = ff := rfl
+example : num.le 2 2 = tt := rfl
+example : num.le 2 3 = tt := rfl
+example : num.le 2 4 = tt := rfl
+example : num.le 2 5 = tt := rfl
 
-example : le 3 0 = ff := rfl
-example : le 3 1 = ff := rfl
-example : le 3 2 = ff := rfl
-example : le 3 3 = tt := rfl
-example : le 3 4 = tt := rfl
-example : le 3 5 = tt := rfl
+example : num.le 3 0 = ff := rfl
+example : num.le 3 1 = ff := rfl
+example : num.le 3 2 = ff := rfl
+example : num.le 3 3 = tt := rfl
+example : num.le 3 4 = tt := rfl
+example : num.le 3 5 = tt := rfl
 
-example : le 4 0 = ff := rfl
-example : le 4 1 = ff := rfl
-example : le 4 2 = ff := rfl
-example : le 4 3 = ff := rfl
-example : le 4 4 = tt := rfl
-example : le 4 5 = tt := rfl
+example : num.le 4 0 = ff := rfl
+example : num.le 4 1 = ff := rfl
+example : num.le 4 2 = ff := rfl
+example : num.le 4 3 = ff := rfl
+example : num.le 4 4 = tt := rfl
+example : num.le 4 5 = tt := rfl
 
-example : le 5 0 = ff := rfl
-example : le 5 1 = ff := rfl
-example : le 5 2 = ff := rfl
-example : le 5 3 = ff := rfl
-example : le 5 4 = ff := rfl
-example : le 5 5 = tt := rfl
-example : le 5 6 = tt := rfl
+example : num.le 5 0 = ff := rfl
+example : num.le 5 1 = ff := rfl
+example : num.le 5 2 = ff := rfl
+example : num.le 5 3 = ff := rfl
+example : num.le 5 4 = ff := rfl
+example : num.le 5 5 = tt := rfl
+example : num.le 5 6 = tt := rfl
 
-example : 0 - 0 = 0 := rfl
-example : 0 - 1 = 0 := rfl
-example : 0 - 2 = 0 := rfl
-example : 0 - 3 = 0 := rfl
+example : num.sub 0 0 = 0 := rfl
+example : num.sub 0 1 = 0 := rfl
+example : num.sub 0 2 = 0 := rfl
+example : num.sub 0 3 = 0 := rfl
 
-example : 1 - 0 = 1 := rfl
-example : 1 - 1 = 0 := rfl
-example : 1 - 2 = 0 := rfl
-example : 1 - 3 = 0 := rfl
+example : num.sub 1 0 = 1 := rfl
+example : num.sub 1 1 = 0 := rfl
+example : num.sub 1 2 = 0 := rfl
+example : num.sub 1 3 = 0 := rfl
 
-example : 2 - 0 = 2 := rfl
-example : 2 - 1 = 1 := rfl
-example : 2 - 2 = 0 := rfl
-example : 2 - 3 = 0 := rfl
-example : 2 - 4 = 0 := rfl
+example : num.sub 2 0 = 2 := rfl
+example : num.sub 2 1 = 1 := rfl
+example : num.sub 2 2 = 0 := rfl
+example : num.sub 2 3 = 0 := rfl
+example : num.sub 2 4 = 0 := rfl
 
-example : 3 - 0 = 3 := rfl
-example : 3 - 1 = 2 := rfl
-example : 3 - 2 = 1 := rfl
-example : 3 - 3 = 0 := rfl
-example : 3 - 4 = 0 := rfl
-example : 3 - 5 = 0 := rfl
+example : num.sub 3 0 = 3 := rfl
+example : num.sub 3 1 = 2 := rfl
+example : num.sub 3 2 = 1 := rfl
+example : num.sub 3 3 = 0 := rfl
+example : num.sub 3 4 = 0 := rfl
+example : num.sub 3 5 = 0 := rfl
 
-example : 4 - 0 = 4 := rfl
-example : 4 - 1 = 3 := rfl
-example : 4 - 2 = 2 := rfl
-example : 4 - 3 = 1 := rfl
-example : 4 - 4 = 0 := rfl
-example : 4 - 5 = 0 := rfl
+example : num.sub 4 0 = 4 := rfl
+example : num.sub 4 1 = 3 := rfl
+example : num.sub 4 2 = 2 := rfl
+example : num.sub 4 3 = 1 := rfl
+example : num.sub 4 4 = 0 := rfl
+example : num.sub 4 5 = 0 := rfl
 
-example : 5 - 0 = 5 := rfl
-example : 5 - 1 = 4 := rfl
-example : 5 - 2 = 3 := rfl
-example : 5 - 3 = 2 := rfl
-example : 5 - 4 = 1 := rfl
-example : 5 - 5 = 0 := rfl
+example : num.sub 5 0 = 5 := rfl
+example : num.sub 5 1 = 4 := rfl
+example : num.sub 5 2 = 3 := rfl
+example : num.sub 5 3 = 2 := rfl
+example : num.sub 5 4 = 1 := rfl
+example : num.sub 5 5 = 0 := rfl
 
-example : 11 - 5 = 6 := rfl
-example : 5 - 11 = 0 := rfl
-example : 12 - 7 = 5 := rfl
-example : 120 - 12 = 108 := rfl
-example : 111 - 11 = 100 := rfl
+example : num.sub 11 5 = 6 := rfl
+example : num.sub 5 11 = 0 := rfl
+example : num.sub 12 7 = 5 := rfl
+example : num.sub 120 12 = 108 := rfl
+example : num.sub 111 11 = 100 := rfl

tests/lean/run/occurs_check_bug1.lean

@@ -3,8 +3,8 @@ import logic data.nat data.prod
 open nat prod
 open decidable
 
-constant modulo (x : ℕ) (y : ℕ) : ℕ
-infixl `mod` := modulo
+constant modulo1 (x : ℕ) (y : ℕ) : ℕ
+infixl `mod` := modulo1
 
 constant gcd_aux : ℕ × ℕ → ℕ
 

tests/lean/run/one.lean

@@ -1,8 +1,8 @@
-inductive one.{l} : Type.{max 1 l} :=
-unit : one.{l}
+inductive one1.{l} : Type.{max 1 l} :=
+unit : one1.{l}
 
 set_option pp.universes true
-check one
+check one1
 
 
 inductive one2.{l} : Type.{max 1 l} :=

tests/lean/run/one2.lean

@@ -1,7 +1,7 @@
 import data.num
 
-inductive one.{l} : Type.{l} :=
-unit : one
+inductive one1.{l} : Type.{l} :=
+unit : one1
 
 inductive pone : Type.{0} :=
 unit : pone
@@ -17,7 +17,7 @@ inductive wrap2.{l} (A : Type.{l}) : Type.{max 1 l} :=
 mk : A → wrap2 A
 
 set_option pp.universes true
-check @one.rec
+check @one1.rec
 check @pone.rec
 check @two.rec
 check @wrap.rec

tests/lean/run/over_subst.lean

@@ -15,12 +15,12 @@ namespace int
 constant int : Type.{1}
 constant add : int → int → int
 constant le : int → int → Prop
-constant one : int
+constant one1 : int
 infixl `+` := add
 infix `≤`  := le
 axiom add_assoc (a b c : int) : (a + b) + c = a + (b + c)
 axiom add_le_left {a b : int} (H : a ≤ b) (c : int) : c + a ≤ c + b
-definition lt (a b : int) := a + one ≤ b
+definition lt (a b : int) := a + one1 ≤ b
 infix `<`  := lt
 end int
 
@@ -28,5 +28,5 @@ open int
 open nat
 open eq
 theorem add_lt_left {a b : int} (H : a < b) (c : int) : c + a < c + b :=
-subst (symm (add_assoc c a one)) (add_le_left H c)
+subst (symm (add_assoc c a one1)) (add_le_left H c)
 end experiment

tests/lean/run/pickle1.lean

@@ -3,5 +3,5 @@ open encodable decidable bool prod list nat option
 variable l : list (nat × bool)
 check encode l
 eval encode [2, 1]
-example : decode (list nat) (encode [1, 1]) = some [1, 1] :=
+example : decode (list nat) (encode [(1:nat), 1]) = some [1, 1] :=
 rfl

tests/lean/run/ppbeta.lean

@@ -1,9 +1,9 @@
 import data.int
-open [coercions] int
+open [coercions] [classes] int
 open [coercions] nat
 
-definition lt (a b : int) := int.le (int.add a 1) b
-infix `<`     := lt
+definition lt1 (a b : int) := int.le (int.add a 1) b
+infix `<`     := lt1
 infixl `+` := int.add
 
 theorem lt_add_succ2 (a : int) (n : nat) : a < a + nat.succ n :=

tests/lean/run/ptst.lean

@@ -1,5 +1,5 @@
-import logic data.prod
-open prod
+import data.nat logic data.prod
+open prod nat
 
 -- Test tuple notation
-check (3, false, 1, true)
+check ((3:nat), false, (1:num), true)

tests/lean/run/rat_coe.lean

@@ -1,5 +1,5 @@
 import data.rat
-open rat
+open rat int
 
 attribute rat.of_int [coercion]
 

tests/lean/run/rat_rfl.lean

@@ -1,7 +1,5 @@
 import data.rat
 open rat
 
-attribute rat.of_int [coercion]
-
-example : 1 + 2⁻¹ + 3 = 3 + 2⁻¹ + 1⁻¹ :=
+example : (1:rat) + 2⁻¹ + 3 = 3 + 2⁻¹ + 1⁻¹ :=
 rfl

tests/lean/run/reducible.lean

@@ -1,7 +1,9 @@
-definition x [reducible]   := 10
-definition y               := 20
-definition z [irreducible] := 30
-definition w               := 40
+open nat
+definition x [reducible]   := (10:nat)
+definition y               := (20:nat)
+definition z [irreducible] := (30:nat)
+definition w               := (40:nat)
+
 
 (*
  local env   = get_env()
@@ -21,8 +23,6 @@ definition w               := 40
  assert(tc:whnf(w) == w)
  -- Opaque and definitions marked as irreducibled are not unfolded
  local tc  = non_irreducible_type_checker(env)
- assert(tc:whnf(x) == val_x)
- assert(tc:whnf(y) == val_y)
  assert(tc:whnf(z) == z)
  -- Only definitions marked as reducible are unfolded
  local tc  = reducible_type_checker(env)
@@ -30,12 +30,6 @@ definition w               := 40
  assert(tc:whnf(y) == y)
  assert(tc:whnf(z) == z)
  assert(tc:whnf(w) == w)
- -- Default: only opaque definitions are not unfolded.
- -- Opaqueness is a feature of the kernel.
- local tc  = type_checker(env)
- assert(tc:whnf(x) == val_x)
- assert(tc:whnf(y) == val_y)
- assert(tc:whnf(z) == val_z)
 *)
 
 eval [whnf] x

tests/lean/run/rewrite8.lean

@@ -3,4 +3,4 @@ open nat
 constant f : nat → nat
 
 theorem tst1 (x y : nat) (H1 : (λ z, z + 0) x = y) : f x = f y :=
-by rewrite [▸* at H1, ^add at H1, H1]
+by rewrite [▸* at H1, add_zero at H1, H1]

tests/lean/run/rewriter12.lean

@@ -3,7 +3,7 @@ open nat
 constant f : nat → nat
 
 example (x y : nat) (H1 : (λ z, z + 0) x = y) : f x = f y :=
-by rewrite [▸* at H1, ^ [add, nat.rec_on, of_num] at H1, H1]
+by rewrite [▸* at H1, add_zero at H1, H1]
 
 example (x y : nat) (H1 : (λ z, z + 0) x = y) : f x = f y :=
-by rewrite [▸* at H1, ↑[add, nat.rec_on, of_num] at H1, H1]
+by rewrite [▸* at H1, add_zero at H1, H1]

tests/lean/run/rewriter14.lean

@@ -8,5 +8,5 @@ attribute of_num [unfold 1]
 
 example (x y : nat) (H1 : f x 0 0 = 0) : x = 0 :=
 begin
-  rewrite [▸* at H1, 4>add_zero at H1, H1]
+  rewrite [↑f at H1, 4>add_zero at H1, H1]
 end

tests/lean/run/secnot.lean

@@ -16,10 +16,10 @@ namespace list
 section
 variable {T : Type}
 notation `[` l:(foldr `,` (h t, cons h t) nil) `]` := l
-check [10, 20, 30]
+check [(10:num), 20, 30]
 end
 end list
 
 open list
-check [10, 20, 40]
-check 10 ◀ 20
+check [(10:num), 20, 40]
+check (10:num) ◀ 20

tests/lean/run/set.lean

@@ -1,7 +1,7 @@
 import logic
-open bool
+open bool nat
 
 definition set {{T : Type}} := T → bool
 infix `∈` := λx A, A x = tt
 
-check 1 ∈ (λ x, tt)
+check 1 ∈ (λ x : nat, tt)

tests/lean/run/show2.lean

@@ -1,7 +1,7 @@
 import data.nat
 open nat
 
-example : ∀ a b, a + b = b + a :=
+example : ∀ a b : nat, a + b = b + a :=
 show ∀ a b : nat, a + b = b + a
 | 0        0        := rfl
 | 0        (succ b) := by rewrite zero_add

tests/lean/run/st_options.lean

@@ -1,24 +1,6 @@
 set_option structure.eta_thm true
 set_option structure.proj_mk_thm true
 
-structure has_mul [class] (A : Type) :=
-(mul : A → A → A)
-
-structure has_add [class] (A : Type) :=
-(add : A → A → A)
-
-structure has_one [class] (A : Type) :=
-(one : A)
-
-structure has_zero [class] (A : Type) :=
-(zero : A)
-
-structure has_inv [class] (A : Type) :=
-(inv : A → A)
-
-structure has_neg [class] (A : Type) :=
-(neg : A → A)
-
 structure semigroup [class] (A : Type) extends has_mul A :=
 (mul_assoc : ∀a b c, mul (mul a b) c = mul a (mul b c))
 

tests/lean/run/struct_inst_exprs.lean

@@ -7,11 +7,11 @@ definition s : nat × nat := pair 10 20
 structure test :=
 (A : Type) (a : A) (B : A → Type) (b : B a)
 
-definition s2 := ⦃ test, a := 3, b := 10 ⦄
+definition s2 := ⦃ test, a := (3:nat), b := (10:nat) ⦄
 
 eval s2
 
-definition s3 := {| test, a := 20, s2 |}
+definition s3 := {| test, a := (20:nat), s2 |}
 
 eval s3
 

tests/lean/run/tactic23.lean

@@ -19,13 +19,12 @@ definition num_to_nat (n : num) : nat
 := num.rec zero (λ n, pos_num_to_nat n) n
 attribute num_to_nat [coercion]
 
--- Now we can write 2 + 3, the coercion will be applied
-check 2 + 3
+check (2:num) + 3
 
 -- Define an assump as an alias for the eassumption tactic
 definition assump : tactic := tactic.eassumption
 
-theorem T1 {p : nat → Prop} {a : nat } (H : p (a+2)) : ∃ x, p (succ x)
+theorem T1 {p : nat → Prop} {a : nat } (H : p (a+(2:num))) : ∃ x, p (succ x)
 := by apply exists.intro; assump
 
 definition is_zero (n : nat)

tests/lean/run/tree.lean

@@ -5,8 +5,8 @@ inductive tree (A : Type) :=
 | leaf : A → tree A
 | node : tree A → tree A → tree A
 
-inductive one.{l} : Type.{max 1 l} :=
-star : one
+inductive one1.{l} : Type.{max 1 l} :=
+star : one1
 
 set_option pp.universes true
 
@@ -17,7 +17,7 @@ namespace manual
     variable {A : Type.{l₁}}
     variable (C : tree A → Type.{l₂})
     definition below (t : tree A) : Type :=
-    tree.rec_on t (λ a, one.{l₂}) (λ t₁ t₂ r₁ r₂, C t₁ × C t₂ × r₁ × r₂)
+    tree.rec_on t (λ a, one1.{l₂}) (λ t₁ t₂ r₁ r₂, C t₁ × C t₂ × r₁ × r₂)
   end
 
   section
@@ -27,7 +27,7 @@ namespace manual
     definition below_rec_on (t : tree A) (H : Π (n : tree A), below C n → C n) : C t
     := have general : C t × below C t, from
         tree.rec_on t
-          (λa, (H (leaf a) one.star, one.star))
+          (λa, (H (leaf a) one1.star, one1.star))
           (λ (l r : tree A) (Hl : C l × below C l) (Hr : C r × below C r),
             have b : below C (node l r), from
               (pr₁ Hl, pr₁ Hr, pr₂ Hl, pr₂ Hr),

tests/lean/run/tree2.lean

@@ -5,8 +5,8 @@ inductive tree (A : Type) :=
 | leaf : A → tree A
 | node : tree A → tree A → tree A
 
-inductive one.{l} : Type.{max 1 l} :=
-star : one
+inductive one1.{l} : Type.{max 1 l} :=
+star : one1
 
 set_option pp.universes true
 
@@ -17,7 +17,7 @@ namespace tree
     variable {A : Type.{l₁}}
     variable (C : tree A → Type.{l₂})
     definition below (t : tree A) : Type :=
-    tree.rec_on t (λ a, one.{l₂}) (λ t₁ t₂ r₁ r₂, C t₁ × C t₂ × r₁ × r₂)
+    tree.rec_on t (λ a, one1.{l₂}) (λ t₁ t₂ r₁ r₂, C t₁ × C t₂ × r₁ × r₂)
   end
 
   section
@@ -27,7 +27,7 @@ namespace tree
     definition below_rec_on (t : tree A) (H : Π (n : tree A), below C n → C n) : C t
     := have general : C t × below C t, from
         tree.rec_on t
-          (λa, (H (leaf a) one.star, one.star))
+          (λa, (H (leaf a) one1.star, one1.star))
           (λ (l r : tree A) (Hl : C l × below C l) (Hr : C r × below C r),
             have b : below C (node l r), from
               (pr₁ Hl, pr₁ Hr, pr₂ Hl, pr₂ Hr),

tests/lean/run/tree3.lean

@@ -5,8 +5,8 @@ inductive tree (A : Type) :=
 | leaf : A → tree A
 | node : tree A → tree A → tree A
 
-inductive one.{l} : Type.{max 1 l} :=
-star : one
+inductive one1.{l} : Type.{max 1 l} :=
+star : one1
 
 set_option pp.universes true
 
@@ -17,7 +17,7 @@ namespace tree
     variable {A : Type.{l₁}}
     variable (C : tree A → Type.{l₂})
     definition below (t : tree A) : Type :=
-    tree.rec_on t (λ a, one.{l₂}) (λ t₁ t₂ r₁ r₂, C t₁ × C t₂ × r₁ × r₂)
+    tree.rec_on t (λ a, one1.{l₂}) (λ t₁ t₂ r₁ r₂, C t₁ × C t₂ × r₁ × r₂)
   end
 
   section
@@ -27,7 +27,7 @@ namespace tree
     definition below_rec_on (t : tree A) (H : Π (n : tree A), below C n → C n) : C t
     := have general : C t × below C t, from
         tree.rec_on t
-          (λa, (H (leaf a) one.star, one.star))
+          (λa, (H (leaf a) one1.star, one1.star))
           (λ (l r : tree A) (Hl : C l × below C l) (Hr : C r × below C r),
             have b : below C (node l r), from
               (pr₁ Hl, pr₁ Hr, pr₂ Hl, pr₂ Hr),

tests/lean/run/tree_height.lean

@@ -1,5 +1,5 @@
 import logic data.nat
-open eq.ops nat
+open eq.ops nat algebra
 
 inductive tree (A : Type) :=
 | leaf : A → tree A
@@ -27,10 +27,10 @@ lt_succ_of_le (le_max_right (height t₁) (height t₂))
 theorem height_lt.trans {A : Type} : transitive (@height_lt A) :=
 inv_image.trans lt height @lt.trans
 
-example : height_lt (leaf 2) (node (leaf 1) (leaf 2)) :=
+example : height_lt (leaf (2:nat)) (node (leaf 1) (leaf 2)) :=
 !height_lt.node_right
 
-example : height_lt  (leaf 2) (node (node (leaf 1) (leaf 2)) (leaf 3)) :=
+example : height_lt  (leaf (2:nat)) (node (node (leaf 1) (leaf 2)) (leaf 3)) :=
 height_lt.trans !height_lt.node_right !height_lt.node_left
 
 end tree

tests/lean/run/tree_subterm_pred.lean

@@ -36,11 +36,11 @@ definition subterm {A : Type} : tree A → tree A → Prop := tc (@direct_subter
 
 definition subterm.wf {A : Type} : well_founded (@subterm A) :=
 tc.wf (@direct_subterm.wf A)
-
-example : subterm (leaf 2) (node (leaf 1) (leaf 2)) :=
+open nat
+example : subterm (leaf (2:nat)) (node (leaf 1) (leaf 2)) :=
 !tc.base !direct_subterm.node_r
 
-example : subterm (leaf 2) (node (node (leaf 1) (leaf 2)) (leaf 3)) :=
+example : subterm (leaf (2:nat)) (node (node (leaf 1) (leaf 2)) (leaf 3)) :=
 have s₁ : subterm (leaf 2) (node (leaf 1) (leaf 2)), from
   !tc.base !direct_subterm.node_r,
 have s₂ : subterm (node (leaf 1) (leaf 2)) (node (node (leaf 1) (leaf 2)) (leaf 3)), from

tests/lean/run/trick.lean

@@ -1,7 +1,7 @@
 import logic
 
 definition proj1 (x : num) (y : num) := x
-definition One := 1
+definition One : num := 1
 
 (*
 local num   = Const("num")

tests/lean/run/tt1.lean

@@ -1,7 +1,7 @@
 import data.prod data.num logic.quantifiers
-open prod
+open prod nat
 
-check (true, false, 10)
+check (true, false, (10:nat))
 
 -- definition a f := f
 

tests/lean/run/unfold_rec.lean

@@ -7,8 +7,6 @@ variable {n : nat}
 theorem tst1 : ∀ n m, succ n + succ m = succ (succ (n + m)) :=
 begin
   intro n m,
-  esimp [add],
-  state,
   rewrite [succ_add]
 end
 

tests/lean/run/unzip_bug.lean

@@ -10,5 +10,5 @@ definition unzip : Π {n : nat}, vector (A × B) n → vector A n × vector B n
    (va, vb) := (a :: va, b :: vb)
   end
 
-example : unzip ((1, 20) :: (2, 30) :: nil) = (1 :: 2 :: nil, 20 :: 30 :: nil) :=
+example : unzip ((1, 20) :: ((2, 30) : nat × nat) :: nil) = (1 :: 2 :: nil, 20 :: 30 :: nil) :=
 rfl

tests/lean/run/vector.lean

@@ -75,7 +75,7 @@ namespace vector
       (λ (n₁ : nat) (a₁ : A) (v₁ : vector A n₁) (B : bw (vcons a₁ v₁)),
          vcons a₁ (pr₁ B)))
 
-  example : append (1 :: 2 :: vnil) (3 :: vnil) = 1 :: 2 :: 3 :: vnil :=
+  example : append ((1:nat) :: 2 :: vnil) (3 :: vnil) = 1 :: 2 :: 3 :: vnil :=
   rfl
 
   definition head {A : Type} {n : nat} (v : vector A (succ n)) : A :=