chore: more simp lemmas for LawfulGetElem (#8470)

This PR adds `@[simp]` to `getElem_pos/neg` (similarly for `getElem!`).
These are often already simp lemmas for concrete types.

Author: kim-em

src/Init/GetElem.lean

@@ -164,25 +164,25 @@ export LawfulGetElem (getElem?_def getElem!_def)
 instance (priority := low) [GetElem coll idx elem valid] [∀ xs i, Decidable (valid xs i)] :
     LawfulGetElem coll idx elem valid where
 
-theorem getElem?_pos [GetElem? cont idx elem dom] [LawfulGetElem cont idx elem dom]
+@[simp] theorem getElem?_pos [GetElem? cont idx elem dom] [LawfulGetElem cont idx elem dom]
     (c : cont) (i : idx) (h : dom c i) : c[i]? = some (c[i]'h) := by
   have : Decidable (dom c i) := .isTrue h
   rw [getElem?_def]
   exact dif_pos h
 
-theorem getElem?_neg [GetElem? cont idx elem dom] [LawfulGetElem cont idx elem dom]
+@[simp] theorem getElem?_neg [GetElem? cont idx elem dom] [LawfulGetElem cont idx elem dom]
     (c : cont) (i : idx) (h : ¬dom c i) : c[i]? = none := by
   have : Decidable (dom c i) := .isFalse h
   rw [getElem?_def]
   exact dif_neg h
 
-theorem getElem!_pos [GetElem? cont idx elem dom] [LawfulGetElem cont idx elem dom]
+@[simp] theorem getElem!_pos [GetElem? cont idx elem dom] [LawfulGetElem cont idx elem dom]
     [Inhabited elem] (c : cont) (i : idx) (h : dom c i) :
     c[i]! = c[i]'h := by
   have : Decidable (dom c i) := .isTrue h
   simp [getElem!_def, getElem?_def, h]
 
-theorem getElem!_neg [GetElem? cont idx elem dom] [LawfulGetElem cont idx elem dom]
+@[simp] theorem getElem!_neg [GetElem? cont idx elem dom] [LawfulGetElem cont idx elem dom]
     [Inhabited elem] (c : cont) (i : idx) (h : ¬dom c i) : c[i]! = default := by
   have : Decidable (dom c i) := .isFalse h
   simp [getElem!_def, getElem?_def, h]
@@ -243,12 +243,12 @@ grind_pattern getElem_of_getElem? => c[i]?, some e
 @[simp] theorem some_getElem_eq_getElem?_iff [GetElem? cont idx elem dom] [LawfulGetElem cont idx elem dom]
     {c : cont} {i : idx} [Decidable (dom c i)] (h : dom c i):
     (some c[i] = c[i]?) ↔ True := by
-  simpa [some_eq_getElem?_iff, h] using ⟨h, trivial⟩
+  simp [h]
 
 @[simp] theorem getElem?_eq_some_getElem_iff [GetElem? cont idx elem dom] [LawfulGetElem cont idx elem dom]
     {c : cont} {i : idx} [Decidable (dom c i)] (h : dom c i):
     (c[i]? = some c[i]) ↔ True := by
-  simpa [getElem?_eq_some_iff, h] using ⟨h, trivial⟩
+  simp [h]
 
 @[deprecated getElem?_eq_none_iff (since := "2025-02-17")]
 abbrev getElem?_eq_none := @getElem?_eq_none_iff
@@ -339,7 +339,8 @@ instance : GetElem? (List α) Nat α fun as i => i < as.length where
 @[simp] theorem get!Internal_eq_getElem! [Inhabited α] {l : List α} {i : Nat} :
     l.get!Internal i = l[i]! := rfl
 
-@[simp] theorem getElem?_eq_getElem {l : List α} {i} (h : i < l.length) :
+-- This is only needed locally; after the `LawfulGetElem` instance the general `getElem?_pos` lemma applies.
+@[local simp] theorem getElem?_eq_getElem {l : List α} {i} (h : i < l.length) :
     l[i]? = some l[i] := by
   induction l generalizing i with
   | nil => cases h

src/Std/Tactic/BVDecide/LRAT/Internal/Clause.lean

@@ -278,7 +278,7 @@ theorem ofArray.folder_foldl_mem_of_mem
           · next hfoo =>
             rw [hl]
             cases x
-            simp [Std.HashMap.getElem?_insertIfNew]
+            simp [Std.HashMap.getElem_insertIfNew]
             intro hbar
             exfalso
             apply hfoo