feat(library/standard/classical): add Peirce's law

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

library/standard/classical.lean

@@ -154,3 +154,8 @@ theorem not_forall_exists {A : Type} {P : A → Bool} (H : ¬ ∀ x, P x) : ∃
      have H2 : ∀ x, ¬ ¬ P x, from not_exists_forall H1,
      have H3 : ∀ x, P x, from take x, not_not_elim (H2 x),
      absurd H3 H)
+
+theorem peirce (a b : Bool) : ((a → b) → a) → a
+:= assume H, by_contradiction (λ Hna : ¬ a,
+     have Hnna : ¬ ¬ a, from not_implies_left (mt H Hna),
+     absurd (not_not_elim Hnna) Hna)

library/standard/logic.lean

@@ -42,6 +42,12 @@ theorem absurd_not_true (H : ¬ true) : false
 theorem not_false_trivial : ¬ false
 := assume H : false, H
 
+theorem not_implies_left {a b : Bool} (H : ¬ (a → b)) : ¬ ¬ a
+:= assume Hna : ¬ a, absurd (assume Ha : a, absurd_elim b Ha Hna) H
+
+theorem not_implies_right {a b : Bool} (H : ¬ (a → b)) : ¬ b
+:= assume Hb : b, absurd (assume Ha : a, Hb) H
+
 inductive and (a b : Bool) : Bool :=
 | and_intro : a → b → and a b