fix(library/elaborator): bug reported by Jeremy Avigad

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

src/builtin/kernel.lean

@@ -809,7 +809,7 @@ theorem inhabited_fun (A : (Type U)) {B : (Type U)} (H : inhabited B) : inhabite
 
 theorem exists_to_eps {A : (Type U)} {P : A → Bool} (H : ∃ x, P x) : P (ε (inhabited_ex_intro H) P)
 := obtain (w : A) (Hw : P w), from H,
-      eps_ax (inhabited_ex_intro H) w Hw
+      @eps_ax _ (inhabited_ex_intro H) P w Hw
 
 theorem axiom_of_choice {A : (Type U)} {B : A → (Type U)} {R : ∀ x : A, B x → Bool} (H : ∀ x, ∃ y, R x y) : ∃ f, ∀ x, R x (f x)
 := exists_intro
@@ -819,7 +819,7 @@ theorem axiom_of_choice {A : (Type U)} {B : A → (Type U)} {R : ∀ x : A, B x
 theorem skolem_th {A : (Type U)} {B : A → (Type U)} {P : ∀ x : A, B x → Bool} :
         (∀ x, ∃ y, P x y) ↔ ∃ f, (∀ x, P x (f x))
 := iff_intro
-      (λ H : (∀ x, ∃ y, P x y), axiom_of_choice H)
+      (λ H : (∀ x, ∃ y, P x y), @axiom_of_choice _ _ P H)
       (λ H : (∃ f, (∀ x, P x (f x))),
              take x, obtain (fw : ∀ x, B x) (Hw : ∀ x, P x (fw x)), from H,
                   exists_intro (fw x) (Hw x))

src/library/elaborator/elaborator.cpp

@@ -895,7 +895,8 @@ class elaborator::imp {
            The constraint is solved by assigning ?m to (fun x1 ... xn, c).
            The arguments may contain duplicate occurrences of variables.
 
-
+        The following case is INCORRECT, and restricts the set of solutions that can be found.
+        IT WAS DISABLED.
         2) a constraint of the form
                ctx |- (?m x1 ... xn) ≈ (f x1 ... xn)      where f does not contain x1 ... xn, and x1 ... xn are distinct
            The constraint is solved by assigning ?m to f OR ?m to (fun x1 ... xn, f x1 ... xn)
@@ -922,6 +923,14 @@ class elaborator::imp {
                 push_new_eq_constraint(ctx, m, s, new_jst);
                 return true;
             } else {
+                return false;
+                #if 0
+                // This code was disabled because it removes valid solutions.
+                // For example, when this piece of code is enabled, we can't
+                // solve
+                //    theorem or_imp (p q : Bool) : (p ∨ q) ↔ (¬ p → q)
+                //    := subst (symm (imp_or (¬ p) q)) (not_not_eq p)
+                // TODO(Leo): delete this piece of code
                 lean_assert(eq_app);
                 expr f = arg(b, 0);
                 std::unique_ptr<generic_case_split> new_cs(new generic_case_split(c, m_state));
@@ -946,6 +955,7 @@ class elaborator::imp {
                 lean_assert(r);
                 m_case_splits.push_back(std::move(new_cs));
                 return r;
+                #endif
             }
         } else {
             return false;

tests/lean/elab4.lean.expected.out

@@ -15,6 +15,6 @@ variable R {A A' : Type}
     {B' : A' → Type}
     (H : @eq Type (∀ x : A, B x) (∀ x : A', B' x))
     (a : A) :
-    @eq Type (B a) (B' (@C A A' (@D A A' B B' H) a))
+    @eq Type (B a) (B' (@C A A' (@D A A' (λ x : A, B x) (λ x : A', B' x) H) a))
 theorem R2 (A1 A2 B1 B2 : Type) (H : @eq Type (A1 → B1) (A2 → B2)) (a : A1) : @eq Type B1 B2 :=
     @R A1 A2 (λ x : A1, B1) (λ x : A2, B2) H a

tests/lean/elab5.lean.expected.out

@@ -15,6 +15,6 @@ variable R {A A' : Type}
     {B' : A' → Type}
     (H : @eq Type (∀ x : A, B x) (∀ x : A', B' x))
     (a : A) :
-    @eq Type (B a) (B' (@C A A' (@D A A' B B' H) a))
+    @eq Type (B a) (B' (@C A A' (@D A A' (λ x : A, B x) (λ x : A', B' x) H) a))
 theorem R2 (A1 A2 B1 B2 : Type) (H : @eq Type (A1 → B1) (A2 → B2)) (a : A1) : @eq Type B1 B2 :=
     @R A1 A2 (λ x : A1, B1) (λ x : A2, B2) H a

tests/lean/elab7.lean.expected.out

@@ -9,8 +9,9 @@
   Assumed: H
   Assumed: a
 eta (F2 a) : (λ x : B, F2 a x) = F2 a
-funext (λ a : A, trans (symm (eta (F1 a))) (trans (funext (λ b : B, H a b)) (eta (F2 a)))) : F1 = F2
-funext (λ a : A, funext (λ b : B, H a b)) : F1 = F2
+funext (λ a : A, trans (symm (eta (F1 a))) (trans (funext (λ b : B, H a b)) (eta (F2 a)))) :
+    (λ x : A, F1 x) = (λ x : A, F2 x)
+funext (λ a : A, funext (λ b : B, H a b)) : (λ (x : A) (x::1 : B), F1 x x::1) = (λ (x : A) (x::1 : B), F2 x x::1)
   Proved: T1
   Proved: T2
   Proved: T3

tests/lean/j5.lean

@@ -0,0 +1,3 @@
+theorem or_imp (p q : Bool) : (p ∨ q) ↔ (¬ p → q)
+:= subst (symm (imp_or (¬ p) q)) (not_not_eq p)
+

tests/lean/j5.lean.expected.out

@@ -0,0 +1,3 @@
+  Set: pp::colors
+  Set: pp::unicode
+  Proved: or_imp

tests/lean/j6.lean

@@ -0,0 +1,8 @@
+theorem symm_iff (p q : Bool) (H : p ↔ q) : (q ↔ p)
+:= symm H
+
+theorem or_imp (p q : Bool) : (p ∨ q) ↔ (¬ p → q)
+:= let H1 := symm_iff _ _ (imp_or (¬ p) q) in
+   let H2 := not_not_eq p in
+   let H3 := subst H1 H2 in
+   H3

tests/lean/j6.lean.expected.out

@@ -0,0 +1,4 @@
+  Set: pp::colors
+  Set: pp::unicode
+  Proved: symm_iff
+  Proved: or_imp