diff --git a/src/Lean/Elab/PreDefinition/Eqns.lean b/src/Lean/Elab/PreDefinition/Eqns.lean
index a293772fda..c169d6d063 100644
--- a/src/Lean/Elab/PreDefinition/Eqns.lean
+++ b/src/Lean/Elab/PreDefinition/Eqns.lean
@@ -95,11 +95,11 @@ private def lhsDependsOn (type : Expr) (fvarId : FVarId) : MetaM Bool :=
 def simpEqnType (eqnType : Expr) : MetaM Expr := do
   forallTelescopeReducing (← instantiateMVars eqnType) fun ys type => do
     let proofVars := collect type
-    trace[Meta.debug] "simpEqnType: {type}"
+    trace[Elab.definition] "simpEqnType type: {type}"
     let mut type ← Match.unfoldNamedPattern type
     let mut eliminated : FVarIdSet := {}
     for y in ys.reverse do
-      trace[Meta.debug] ">> simpEqnType: {← inferType y}, {type}"
+      trace[Elab.definition] ">> simpEqnType: {← inferType y}, {type}"
       if proofVars.contains y.fvarId! then
         let some (_, Expr.fvar fvarId _, rhs) ← matchEq? (← inferType y) | throwError "unexpected hypothesis in altenative{indentExpr eqnType}"
         eliminated := eliminated.insert fvarId
@@ -129,7 +129,7 @@ where
       ST.Prim.Ref.get ref
     runST (go e)
 
-private def saveEqn (mvarId : MVarId) : StateRefT (Array Expr) MetaM Unit := withMVarContext mvarId do
+private partial def saveEqn (mvarId : MVarId) : StateRefT (Array Expr) MetaM Unit := withMVarContext mvarId do
   let target ← getMVarType' mvarId
   let fvarState := collectFVars {} target
   let fvarState ← (← getLCtx).foldrM (init := fvarState) fun decl fvarState => do
@@ -137,20 +137,51 @@ private def saveEqn (mvarId : MVarId) : StateRefT (Array Expr) MetaM Unit := wit
       return collectFVars fvarState (← instantiateMVars decl.type)
     else
       return fvarState
-  let mut fvarSet := fvarState.fvarSet
+  let mut fvarIdSet := fvarState.fvarSet
   let mut fvarIds ← sortFVarIds <| fvarState.fvarSet.toArray
-  -- Include propositions that are not in fvarState.fvarSet, and only contains variables in fvarSet
-  for decl in (← getLCtx) do
-    unless fvarSet.contains decl.fvarId do
-      if (← isProp decl.type) then
-        let type ← instantiateMVars decl.type
-        let missing? := type.find? fun e => e.isFVar && !fvarSet.contains e.fvarId!
-        if missing?.isNone then
-          fvarIds := fvarIds.push decl.fvarId
-          fvarSet := fvarSet.insert decl.fvarId
+  -- Include (relevant) propositions that are not already in `fvarIdSet`
+  let mut modified := false
+  repeat
+    modified := false
+    for decl in (← getLCtx) do
+      unless fvarIdSet.contains decl.fvarId do
+        if (← isProp decl.type) then
+          let type ← instantiateMVars decl.type
+          unless (← isIrrelevant fvarIdSet type) do
+            modified := true
+            (fvarIdSet, fvarIds) ← pushDecl fvarIdSet fvarIds decl
+  until !modified
   let type ← mkForallFVars (fvarIds.map mkFVar) target
   let type ← simpEqnType type
   modify (·.push type)
+where
+  /--
+    We say the type/proposition is "irrelevant" if
+    1- It does not contain any variable in `fvarIdSet` OR
+    2- It is of the form `x = t` or `t = x` where `x` is a free variable
+       that is not in `fvarIdSet`. This can of equality can be eliminated by substitution.  -/
+  isIrrelevant (fvarIdSet : FVarIdSet) (type : Expr) : MetaM Bool := do
+    if Option.isNone <| type.find? fun e => e.isFVar && fvarIdSet.contains e.fvarId! then
+      return true
+    else if let some (_, lhs, rhs) := type.eq? then
+      return (lhs.isFVar && !fvarIdSet.contains lhs.fvarId!)
+             || (rhs.isFVar && !fvarIdSet.contains rhs.fvarId!)
+    else
+      return false
+
+  pushDecl (fvarIdSet : FVarIdSet) (fvarIds : Array FVarId) (localDecl : LocalDecl) : MetaM (FVarIdSet × Array FVarId) := do
+    let (fvarIdSet, fvarIds) ← collectDeps fvarIdSet fvarIds (← instantiateMVars localDecl.type)
+    return (fvarIdSet.insert localDecl.fvarId, fvarIds.push localDecl.fvarId)
+
+  collectDeps (fvarIdSet : FVarIdSet) (fvarIds : Array FVarId) (type : Expr) : MetaM (FVarIdSet × Array FVarId) := do
+    let s := collectFVars {} type
+    let usedFVarIds ← sortFVarIds <| s.fvarSet.toArray
+    let mut fvarIdSet := fvarIdSet
+    let mut fvarIds := fvarIds
+    for fvarId in usedFVarIds do
+      unless fvarIdSet.contains fvarId do
+        (fvarIdSet, fvarIds) ← pushDecl fvarIdSet fvarIds (← getLocalDecl fvarId)
+    return (fvarIdSet, fvarIds)
 
 partial def mkEqnTypes (declNames : Array Name) (mvarId : MVarId) : MetaM (Array Expr) := do
   let (_, eqnTypes) ← go mvarId |>.run { declNames } |>.run #[]
diff --git a/tests/lean/run/streamEqIssue.lean b/tests/lean/run/streamEqIssue.lean
new file mode 100644
index 0000000000..6401c0016e
--- /dev/null
+++ b/tests/lean/run/streamEqIssue.lean
@@ -0,0 +1,9 @@
+@[simp] def Stream.hasLength [Stream stream value] (n : Nat) (s : stream) : Bool :=
+  match n, Stream.next? s with
+  | 0, none => true
+  | n + 1, some (_, s') => hasLength n s'
+  | _, _ => false
+
+#check @Stream.hasLength._eq_1
+#check @Stream.hasLength._eq_2
+#check @Stream.hasLength._eq_3