From eab0456b279d48aba73c03f7a99e77e366e82226 Mon Sep 17 00:00:00 2001
From: Leonardo de Moura <leonardo@microsoft.com>
Date: Thu, 6 Feb 2014 11:33:27 -0800
Subject: [PATCH] test(tests/lean): test super opaque style

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
---
 tests/lean/j3.lean              | 37 +++++++++++++++++++++++++++++++++
 tests/lean/j3.lean.expected.out | 11 ++++++++++
 2 files changed, 48 insertions(+)
 create mode 100644 tests/lean/j3.lean
 create mode 100644 tests/lean/j3.lean.expected.out

diff --git a/tests/lean/j3.lean b/tests/lean/j3.lean
new file mode 100644
index 000000000..3cb5d9b7b
--- /dev/null
+++ b/tests/lean/j3.lean
@@ -0,0 +1,37 @@
+import macros
+import tactic
+using Nat
+
+definition dvd (a b : Nat) : Bool := ∃ c, a * c = b
+infix 50 | : dvd
+theorem dvd_elim {a b : Nat} (H : a | b) : ∃ c, a * c = b  := H
+theorem dvd_intro {a b : Nat} (c : Nat) (H : a * c = b) : a | b := exists_intro c H
+set_opaque dvd true
+
+
+theorem dvd_trans {a b c} (H1 : a | b) (H2 : b | c) : a | c
+:= obtain (w1 : Nat) (Hw1 : a * w1 = b), from dvd_elim H1,
+   obtain (w2 : Nat) (Hw2 : b * w2 = c), from dvd_elim H2,
+     dvd_intro (w1 * w2)
+       (calc a * (w1 * w2) = a * w1 * w2 : symm (mul_assoc a w1 w2)
+                       ... = b * w2 : { Hw1 }
+                       ... = c : Hw2)
+
+
+definition prime p := p ≥ 2 ∧ forall m, m | p → m = 1 ∨ m = p
+
+theorem not_prime_eq (n : Nat) (H1 : n ≥ 2) (H2 : ¬ prime n) : ∃ m, m | n ∧ m ≠ 1 ∧ m ≠ n
+:= have H3 : ¬ n ≥ 2 ∨ ¬ (∀ m : Nat, m | n → m = 1 ∨ m = n),
+     from (not_and _ _ ◂ H2),
+   have H4 : ¬ ¬ n ≥ 2,
+     from ((symm (not_not_eq _)) ◂ H1),
+   obtain (m : Nat) (H5 :  ¬ (m | n → m = 1 ∨ m = n)),
+     from (not_forall_elim (resolve1 H3 H4)),
+   have H6 : m | n ∧ ¬ (m = 1 ∨ m = n),
+     from ((not_implies _ _) ◂ H5),
+   have H7 : ¬ (m = 1 ∨ m = n) ↔ (m ≠ 1 ∧ m ≠ n),
+     from (not_or (m = 1) (m = n)),
+   have H8 : m | n ∧ m ≠ 1 ∧ m ≠ n,
+     from subst H6 H7,
+   show ∃ m, m | n ∧ m ≠ 1 ∧ m ≠ n,
+     from exists_intro m H8
diff --git a/tests/lean/j3.lean.expected.out b/tests/lean/j3.lean.expected.out
new file mode 100644
index 000000000..3440ece17
--- /dev/null
+++ b/tests/lean/j3.lean.expected.out
@@ -0,0 +1,11 @@
+  Set: pp::colors
+  Set: pp::unicode
+  Imported 'macros'
+  Imported 'tactic'
+  Using: Nat
+  Defined: dvd
+  Proved: dvd_elim
+  Proved: dvd_intro
+  Proved: dvd_trans
+  Defined: prime
+  Proved: not_prime_eq