fix: split at h when h has forward dependencies (#4211)

We use an approach similar to the one used in `simp`. 

closes #3731

src/Lean/Meta/Basic.lean

@@ -825,6 +825,17 @@ context. Fails if the given expression is not a fvar or if no such declaration e
 def getFVarLocalDecl (fvar : Expr) : MetaM LocalDecl :=
   fvar.fvarId!.getDecl
 
+/--
+Returns `true` if another local declaration in the local context depends on `fvarId`.
+-/
+def _root_.Lean.FVarId.hasForwardDeps (fvarId : FVarId) : MetaM Bool := do
+  let decl ← fvarId.getDecl
+  (← getLCtx).foldlM (init := false) (start := decl.index + 1) fun found other =>
+    if found then
+      return true
+    else
+      localDeclDependsOn other fvarId
+
 /--
 Given a user-facing name for a free variable, return its declaration in the current local context.
 Throw an exception if free variable is not declared.

src/Lean/Meta/Tactic/Split.lean

@@ -320,10 +320,17 @@ def splitLocalDecl? (mvarId : MVarId) (fvarId : FVarId) : MetaM (Option (List MV
       if e.isIte || e.isDIte then
         return (← splitIfLocalDecl? mvarId fvarId).map fun (mvarId₁, mvarId₂) => [mvarId₁, mvarId₂]
       else
-        let (fvarIds, mvarId) ← mvarId.revert #[fvarId]
-        let num := fvarIds.size
+        let mut mvarId := mvarId
+        let localDecl ← fvarId.getDecl
+        if (← pure localDecl.isLet <||> exprDependsOn (← mvarId.getType) fvarId <||> fvarId.hasForwardDeps) then
+          -- If `fvarId` has dependencies or is a let-decl, we create a copy.
+          mvarId ← mvarId.assert localDecl.userName localDecl.type localDecl.toExpr
+        else
+          let (fvarIds, mvarId') ← mvarId.revert #[fvarId]
+          assert! fvarIds.size == 1 -- fvarId does not have forward dependencies
+          mvarId := mvarId'
         let mvarIds ← splitMatch mvarId e
-        let mvarIds ← mvarIds.mapM fun mvarId => return (← mvarId.introNP num).2
+        let mvarIds ← mvarIds.mapM fun mvarId => return (← mvarId.intro1P).2
         return some mvarIds
     else
       return none

tests/lean/run/3731.lean

@@ -0,0 +1,76 @@
+import Lean.Data.HashMap
+open Lean
+
+/--
+A circuit node declaration. These are not recursive but instead contain indices into an `Env`.
+-/
+inductive Decl where
+  /--
+  A node with a constant output value.
+  -/
+  | const (b : Bool)
+  /--
+  An input node to the circuit.
+  -/
+  | atom (idx : Nat)
+  /--
+  An AIG gate with configurable input nodes and polarity. `l` and `r` are the
+  input node indices while `linv` and `rinv` say whether there is an inverter on
+  the left or right input.
+  -/
+  | gate (l r : Nat) (linv rinv : Bool)
+  deriving BEq, Hashable, DecidableEq
+
+/--
+A cache that is valid with respect to some `Array Decl`.
+-/
+def Cache (_decls : Array Decl) := HashMap Decl Nat
+
+/--
+Lookup a `decl` in a `cache`.
+
+If this returns `some i`, `Cache.find?_poperty` can be used to demonstrate: `decls[i] = decl`.
+-/
+@[irreducible]
+def Cache.find? (cache : Cache decls) (decl : Decl) : Option Nat :=
+  match cache.val.find? decl with
+  | some hit =>
+    if h1:hit < decls.size then
+      if decls[hit]'h1 = decl then
+        some hit
+      else
+        none
+    else
+      none
+  | none => none
+
+/--
+This states that all indices, found in a `Cache` that is valid with respect to some `decls`,
+are within bounds of `decls`.
+-/
+theorem Cache.find?_bounds {decls : Array Decl} {idx : Nat} (c : Cache decls) (decl : Decl)
+    (h : c.find? decl = some idx) : idx < decls.size := by
+  unfold find? at h
+  split at h
+  . split at h
+    . split at h
+      . injection h
+        omega
+      . contradiction
+    . contradiction
+  . contradiction
+
+/--
+This states that if `Cache.find? decl` returns `some i`, `decls[i] = decl`, holds.
+-/
+theorem Cache.find?_property {decls : Array Decl} {idx : Nat} (c : Cache decls) (decl : Decl)
+    (h : c.find? decl = some idx) : decls[idx]'(Cache.find?_bounds c decl h) = decl := by
+  unfold find? at h
+  split at h
+  . split at h
+    . split at h
+      . injection h
+        subst idx; assumption
+      . contradiction
+    . contradiction
+  . contradiction