chore(tests/lean): add missing tests

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

tests/lean/run/coe6.lean

@@ -0,0 +1,15 @@
+import data.unit
+open unit
+
+variable int : Type.{1}
+variable nat : Type.{1}
+variable izero : int
+variable nzero : nat
+variable isucc : int → int
+variable nsucc : nat → nat
+definition f [coercion] (a : unit) : int := izero
+definition g [coercion] (a : unit) : nat := nzero
+
+set_option pp.coercion true
+check isucc star
+check nsucc star

tests/lean/run/coe8.lean

@@ -0,0 +1,16 @@
+import logic
+
+variable nat : Type.{1}
+variable int : Type.{1}
+variable of_nat : nat → int
+coercion of_nat
+variable nat_add : nat → nat → nat
+variable int_add : int → int → int
+infixl `+`:65 := int_add
+infixl `+`:65 := nat_add
+
+print "================"
+variable tst (n m : nat) : @eq int (of_nat n + of_nat m) (n + m)
+
+check tst
+exit

tests/lean/run/ex.lean

@@ -0,0 +1,3 @@
+import standard
+set_option pp.implicit true
+check ∃x, x = 0

tests/lean/run/protected.lean

@@ -0,0 +1,10 @@
+import logic
+
+namespace foo
+  definition C [protected] := true
+  definition D := true
+end foo
+
+open foo
+check foo.C
+check D

tests/lean/run/t3.lean

@@ -0,0 +1,22 @@
+variable int : Type.{1}
+variable nat : Type.{1}
+namespace int
+variable plus : int → int → int
+end int
+
+namespace nat
+variable plus : nat → nat → nat
+end nat
+
+open int nat
+
+variables a b : int
+
+
+check plus a b
+
+variable f : int → int → int
+variable g : nat → nat → int
+notation A `+`:65 B:65 := f A (g B B)
+variable n : nat
+check a + n

tests/lean/run/tac1.lean

@@ -0,0 +1,6 @@
+import tools.tactic
+open tactic
+
+definition mytac := apply @and_intro; apply @refl
+
+check @mytac

tests/lean/run/tt1.lean

@@ -0,0 +1,8 @@
+import data.prod data.num logic.core.quantifiers
+open prod
+
+check (true, false, 10)
+
+-- definition a f := f
+
+check fun x, x ∧ x

tests/lean/slow/nat_bug1.lean

@@ -0,0 +1,23 @@
+----------------------------------------------------------------------------------------------------
+-- Copyright (c) 2014 Floris van Doorn. All rights reserved.
+-- Released under Apache 2.0 license as described in the file LICENSE.
+-- Author: Floris van Doorn
+----------------------------------------------------------------------------------------------------
+import logic
+open tactic num
+
+inductive nat : Type :=
+zero : nat,
+succ : nat → nat
+
+notation `ℕ`:max := nat
+
+abbreviation plus (x y : ℕ) : ℕ
+:= nat_rec x (λ n r, succ r) y
+
+definition to_nat [coercion] [inline] (n : num) : ℕ
+:= num_rec zero (λ n, pos_num_rec (succ zero) (λ n r, plus r (plus r (succ zero))) (λ n r, plus r r) n) n
+
+print "=================="
+theorem nat_rec_zero {P : ℕ → Type} (x : P 0) (f : ∀m, P m → P (succ m)) : nat_rec x f 0 = x :=
+refl _