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lines changed Original file line number Diff line number Diff line change @@ -393,3 +393,71 @@ example {α : Sort u} (h : Empty) : α := by apply? -star
393393-- With `+star`, we find `Empty.elim` via star-indexed lemma fallback.
394394#guard_msgs (drop info) in
395395example {α : Sort u} (h : Empty) : α := by apply? +star
396+
397+ -- Verify that `-star` doesn't break normal (non-star-indexed) lemma search.
398+ section MinusStar
399+
400+ /--
401+ info: Try this:
402+ [ apply ] exact Nat.add_comm x y
403+ -/
404+ #guard_msgs in
405+ example (x y : Nat) : x + y = y + x := by apply? -star
406+
407+ /--
408+ info: Try this:
409+ [ apply ] exact fun a => Nat.add_le_add_right a k
410+ -/
411+ #guard_msgs in
412+ example (n m k : Nat) : n ≤ m → n + k ≤ m + k := by apply? -star
413+
414+ /--
415+ info: Try this:
416+ [ apply ] exact Nat.mul_dvd_mul_left a w
417+ -/
418+ #guard_msgs in
419+ example (_ha : a > 0 ) (w : b ∣ c) : a * b ∣ a * c := by apply? -star
420+
421+ /--
422+ info: Try this:
423+ [ apply ] exact Nat.lt_add_one x
424+ -/
425+ #guard_msgs in
426+ example : x < x + 1 := by exact? -star
427+
428+ /--
429+ info: Try this:
430+ [ apply ] exact eq_comm
431+ -/
432+ #guard_msgs in
433+ example {α : Type } (x y : α) : x = y ↔ y = x := by apply? -star
434+
435+ /--
436+ info: Try this:
437+ [ apply ] exact (p_iff_q a).mp h
438+ -/
439+ #guard_msgs in
440+ example {a : Nat} (h : P a) : Q a := by apply? -star
441+
442+ /--
443+ info: Try this:
444+ [ apply ] exact (Nat.dvd_add_iff_left h₁).mpr h₂
445+ -/
446+ #guard_msgs in
447+ example {a b c : Nat} (h₁ : a ∣ c) (h₂ : a ∣ b + c) : a ∣ b := by apply? -star
448+
449+ /--
450+ info: Try this:
451+ [ apply ] exact L.flatten
452+ -/
453+ #guard_msgs in
454+ example (L : List (List Nat)) : List Nat := by apply? -star using L
455+
456+ /--
457+ info: Try this:
458+ [ apply ] exact Bool_eq_iff
459+ -/
460+ #guard_msgs in
461+ example {A B : Bool} : (A = B) = (A ↔ B) := by apply? -star
462+
463+ end MinusStar
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