feat: add have forms of let_* simp lemmas (#8790)

This PR adds `have` forms of simp lemmas that will be used in a future
`have` simplifier. This depends on #8751 and future elaboration changes,
since these are meant to elaborate using `Expr.letE (nondep := true) ..`
expressions; for now they are duplicates of the `letFun_*` lemmas.

Author: kmill

src/Init/SimpLemmas.lean

@@ -74,6 +74,28 @@ theorem let_body_congr {α : Sort u} {β : α → Sort v} {b b' : (a : α) → 
     (a : α) (h : ∀ x, b x = b' x) : (let x := a; b x) = (let x := a; b' x) :=
   (funext h : b = b') ▸ rfl
 
+theorem have_unused {α : Sort u} {β : Sort v} (a : α) {b b' : β}
+    (h : b = b') : (have _ := a; b) = b' := h
+
+theorem have_unused_dep {α : Sort u} {β : Sort v} (a : α) {b : α → β} {b' : β}
+    (h : ∀ x, b x = b') : (have x := a; b x) = b' := h a
+
+theorem have_congr {α : Sort u} {β : Sort v} {a a' : α} {f f' : α → β}
+    (h₁ : a = a') (h₂ : ∀ x, f x = f' x) : (have x := a; f x) = (have x := a'; f' x) :=
+  @congr α β f f' a a' (funext h₂) h₁
+
+theorem have_val_congr {α : Sort u} {β : Sort v} {a a' : α} {f : α → β}
+    (h : a = a') : (have x := a; f x) = (have x := a'; f x) :=
+  @congrArg α β a a' f h
+
+theorem have_body_congr_dep {α : Sort u} {β : α → Sort v} (a : α) {f f' : (x : α) → β x}
+    (h : ∀ x, f x = f' x) : (have x := a; f x) = (have x := a; f' x) :=
+  h a
+
+theorem have_body_congr {α : Sort u} {β : Sort v} (a : α) {f f' : α → β}
+    (h : ∀ x, f x = f' x) : (have x := a; f x) = (have x := a; f' x) :=
+  h a
+
 theorem letFun_unused {α : Sort u} {β : Sort v} (a : α) {b b' : β} (h : b = b') : @letFun α (fun _ => β) a (fun _ => b) = b' :=
   h