chore: copy over some nth_rewrite tests from mathlib3 (#3462)

There's a somewhat unsatisfactory situation here: when `nth_rewrite` was ported from mathlib3 to mathlib4, its behaviour changed significantly. Now it is "just" a syntax level tactic for accessing the "Occurrences" argument of the underlying rewrite machinery. However in mathlib3 is actually had different behaviour, allowing rewriting in individual locations even when the lemma matched in different ways. (Both Lean 3 and Lean 4 have a stuck metavariables problem in this situation.)

This PR restores the tests from mathlib3, with the ones broken because of this regression just commented out, and an explanation added. Hopefully one day we'll fix this up.



Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

test/NthRewrite.lean

@@ -1,5 +1,7 @@
 import Mathlib.Tactic.NthRewrite
 import Mathlib.Algebra.Group.Defs
+import Mathlib.Data.Vector
+import Mathlib.Data.Nat.Basic
 
 example [AddZeroClass G] {a : G} (h : a = a): a = (a + 0) := by
   nth_rewrite 2 [←add_zero a] at h
@@ -8,4 +10,92 @@ example [AddZeroClass G] {a : G} (h : a = a): a = (a + 0) := by
 example [AddZeroClass G] {a : G} : a + a = a + (a + 0) := by
   nth_rw 2 [←add_zero a]
 
--- Porting note: Port all tests from mathlib3 once `data.nat.basic` and `data.vector` are ported
+structure F :=
+(a : ℕ)
+(v : Vector ℕ a)
+(p : v.val = [])
+
+example (f : F) : f.v.val = [] := by
+  nth_rw 1 [f.p]
+
+structure Cat :=
+  (O : Type)
+  (H : O → O → Type)
+  (i : (o : O) →  H o o)
+  (c : {X Y Z : O} → (f : H X Y) → (g : H Y Z) → H X Z)
+  (li : ∀ {X Y : O} (f : H X Y), c (i X) f = f)
+  (ri : ∀ {X Y : O} (f : H X Y), c f (i Y) = f)
+  (a : ∀ {W X Y Z : O} (f : H W X) (g : H X Y) (h : H Y Z), c (c f g) h = c f (c g h))
+
+example (C : Cat) (W X Y Z : C.O) (f : C.H X Y) (g : C.H W X) (h _k : C.H Y Z) :
+    C.c (C.c g f) h = C.c g (C.c f h) := by
+  nth_rw 1 [C.a]
+
+example (C : Cat) (X Y : C.O) (f : C.H X Y) : C.c f (C.i Y) = f := by
+  nth_rw 1 [C.ri]
+
+-- Porting note: the next test fails because `nth_rewrite` has unfortunately changed behaviour
+-- since mathlib3.
+
+-- example (x y z : ℕ) (h1 : x = y) (h2 : y = z) :
+--   x + x + x + y = y + y + x + x := by
+--   nth_rewrite 3 [h1, h2] -- h2 is not used
+--   nth_rewrite 3 [h2]
+--   repeat { rw [h1] }
+--   repeat { rw [h2] }
+
+axiom foo : [1] = [2]
+
+example : [[1], [1], [1]] = [[1], [2], [1]] := by
+  nth_rw 2 [foo]
+
+axiom foo' : [6] = [7]
+axiom bar' : [[5],[5]] = [[6],[6]]
+
+example : [[7],[6]] = [[5],[5]] := by
+  nth_rewrite 1 [foo']
+  nth_rewrite 1 [bar']
+  nth_rewrite 1 [←foo']
+  nth_rewrite 1 [←foo']
+  rfl
+
+-- Porting note:
+-- The next two tests fail because the `nth_rewrite` we have in mathlib4
+-- is just a syntactic wrapper around the `Occurrences` argument
+-- for the internal rewriting functions,
+-- and not actually a port of the mathlib3 tactic.
+-- Thus is suffers from the exact same problem:
+-- when a lemma matches in several different ways,
+-- we cannot rewrite via the later ones because of stuck metavariables.
+
+-- example (a b c : ℕ) : c + a + b = a + c + b := by
+--   nth_rewrite 4 [add_comm]
+
+-- axiom wowzer : (3, 3) = (5, 2)
+-- axiom kachow (n : ℕ) : (4, n) = (5, n)
+-- axiom pchew (n : ℕ) : (n, 5) = (5, n)
+-- axiom smash (n m : ℕ) : (n, m) = (1, 1)
+
+-- example : [(3, 3), (5, 9), (5, 9)] = [(4, 5), (3, 6), (1, 1)] := by
+--   nth_rewrite 1 [wowzer]
+--   nth_rewrite 3 [←pchew]
+--   nth_rewrite 1 [pchew]
+
+--   nth_rewrite 1 [smash]
+--   nth_rewrite 2 [smash]
+--   nth_rewrite 3 [smash]
+--   nth_rewrite 4 [smash]
+--   nth_rewrite 5 [smash]
+--   nth_rewrite 6 [smash]
+
+example (x y : Prop) (h₁ : x ↔ y) (h₂ : x ↔ x ∧ x) : x ∧ x ↔ x := by
+  nth_rewrite 3 [h₁] at h₂
+  nth_rewrite 1 [← h₁] at h₂
+  nth_rewrite 3 [h₂]
+  rfl
+
+example (x y : ℕ) (h₁ : x = y) (h₂ : x = x + x) : x + x = x := by
+  nth_rewrite 3 [h₁] at h₂
+  nth_rewrite 1 [← h₁] at h₂
+  nth_rewrite 3 [h₂]
+  rfl