diff --git a/src/Lean/Elab/PreDefinition/Structural/Eqns.lean b/src/Lean/Elab/PreDefinition/Structural/Eqns.lean
index 2da2d4366c..347a0cac1a 100644
--- a/src/Lean/Elab/PreDefinition/Structural/Eqns.lean
+++ b/src/Lean/Elab/PreDefinition/Structural/Eqns.lean
@@ -24,6 +24,12 @@ def deltaLHS (mvarId : MVarId) : MetaM MVarId := withMVarContext mvarId do
   let some lhs ← delta? lhs | throwTacticEx `deltaLHS mvarId "failed to delta reduce lhs"
   replaceTargetDefEq mvarId (← mkEq lhs rhs)
 
+def deltaRHS? (mvarId : MVarId) (declName : Name) : MetaM (Option MVarId) := withMVarContext mvarId do
+  let target ← getMVarType' mvarId
+  let some (_, lhs, rhs) ← target.eq? | throwTacticEx `deltaRHS mvarId "equality expected"
+  let some rhs ← delta? rhs (. == declName) | return none
+  replaceTargetDefEq mvarId (← mkEq lhs rhs)
+
 private partial def whnfAux (e : Expr) : MetaM Expr := do
   let e ← whnfR e
   match e with
@@ -77,6 +83,10 @@ private def simpMatch? (mvarId : MVarId) : MetaM (Option MVarId) := do
   let mvarId' ← Split.simpMatchTarget mvarId
   if mvarId != mvarId' then return some mvarId' else return none
 
+private def simpIf? (mvarId : MVarId) : MetaM (Option MVarId) := do
+  let mvarId' ← simpIfTarget mvarId (useDecide := true)
+  if mvarId != mvarId' then return some mvarId' else return none
+
 /--
   Auxiliary method for `mkEqnTypes`. We should "keep going"/"processing" the goal
    `... |- f ... = rhs` at `mkEqnTypes` IF `rhs` contains a `f` application containing loose bound
@@ -124,7 +134,8 @@ private partial def mkEqnTypes (mvarId : MVarId) : ReaderT EqnInfo (StateRefT (A
 private def mkBaseNameFor (env : Environment) (declName : Name) : Name :=
   Lean.mkBaseNameFor env declName `eq_1 `_eqns
 
-private partial def mkProof (declName : Name) (type : Expr) : MetaM Expr :=
+private partial def mkProof (declName : Name) (type : Expr) : MetaM Expr := do
+  trace[Elab.definition.structural.eqns] "proving: {type}"
   withNewMCtxDepth do
     let main ← mkFreshExprSyntheticOpaqueMVar type
     let (_, mvarId) ← intros main.mvarId!
@@ -138,9 +149,13 @@ where
       return ()
     else if (← tryContradiction mvarId) then
       return ()
+    else if let some mvarId ← simpMatch? mvarId then
+      go mvarId
+    else if let some mvarId ← simpIf? mvarId then
+      go mvarId
     else if let some mvarId ← whnfReducibleLHS? mvarId then
       go mvarId
-    else if let some mvarId ← simpMatch? mvarId then
+    else if let some mvarId ← deltaRHS? mvarId declName then
       go mvarId
     else if let some mvarIds ← casesOnStuckLHS? mvarId then
       mvarIds.forM go
diff --git a/tests/lean/run/structuralEqns2.lean b/tests/lean/run/structuralEqns2.lean
new file mode 100644
index 0000000000..298751e185
--- /dev/null
+++ b/tests/lean/run/structuralEqns2.lean
@@ -0,0 +1,17 @@
+import Lean
+
+open Lean
+open Lean.Meta
+def tst (declName : Name) : MetaM Unit := do
+  IO.println (← getEqnsFor? declName)
+
+def g (i j : Nat) : Nat :=
+  if i < 5 then 0 else
+  match j with
+  | Nat.zero => 1
+  | Nat.succ j => g i j
+
+#eval tst ``g
+#check g.eq_1
+#check g.eq_2
+#check g.eq_3