Try this: simp only [f] [Meta.Tactic.simp.rewrite] unfold f, f (a :: b = []) ==> a :: b = [] [Meta.Tactic.simp.rewrite] @eq_self:1000, False = False ==> True Try this: simp only [length] [Meta.Tactic.simp.rewrite] unfold length, length (a :: b :: as) ==> length (b :: as) + 1 [Meta.Tactic.simp.rewrite] unfold length, length (b :: as) ==> length as + 1 Try this: simp only [fact] [Meta.Tactic.simp.rewrite] unfold fact, fact (Nat.succ x) ==> (x + 1) * fact x Try this: simp only [head] [Meta.Tactic.simp.rewrite] unfold head, head (a :: as) ==> match a :: as with | [] => default | a :: tail => a [Meta.Tactic.simp.rewrite] @eq_self:1000, a = a ==> True Try this: simp only [foo] [Meta.Tactic.simp.rewrite] unfold foo, foo ==> 10 [Meta.Tactic.simp.rewrite] @eq_self:1000, 10 + x = 10 + x ==> True Try this: simp only [g, Id.pure_eq] [Meta.Tactic.simp.rewrite] unfold g, g x ==> Id.run (let x := x; pure x) [Meta.Tactic.simp.rewrite] @Id.pure_eq:1000, pure x ==> x Try this: simp only [f1, modify, modifyGet, MonadStateOf.modifyGet, StateT.modifyGet, pure, f2, bind, StateT.bind, get, getThe, MonadStateOf.get, StateT.get, set, StateT.set] [Meta.Tactic.simp.rewrite] unfold f1, f1 ==> modify fun x => g x [Meta.Tactic.simp.rewrite] unfold modify, modify fun x => g x ==> modifyGet fun s => (PUnit.unit, (fun x => g x) s) [Meta.Tactic.simp.rewrite] unfold StateT.modifyGet, StateT.modifyGet fun s => (PUnit.unit, (fun x => g x) s) ==> fun s => pure ((fun s => (PUnit.unit, (fun x => g x) s)) s) [Meta.Tactic.simp.rewrite] unfold f2, f2 ==> do let s ← get set (g s) [Meta.Tactic.simp.rewrite] unfold StateT.bind, StateT.bind get fun s => set (g s) ==> fun s => do let __discr ← get s match __discr with | (a, s) => (fun s => set (g s)) a s [Meta.Tactic.simp.rewrite] unfold getThe, getThe Nat s ==> MonadStateOf.get s [Meta.Tactic.simp.rewrite] unfold StateT.get, StateT.get s ==> pure (s, s) [Meta.Tactic.simp.rewrite] unfold StateT.set, StateT.set (g a) s ==> pure (PUnit.unit, g a) [Meta.Tactic.simp.rewrite] @eq_self:1000, (fun s => (PUnit.unit, g s)) = fun s => (PUnit.unit, g s) ==> True Try this: simp only [bla, h] [Meta.Tactic.simp.rewrite] unfold bla, bla x ==> match h x with | Sum.inl (y, z) => y + z | Sum.inr val => 0 [Meta.Tactic.simp.rewrite] unfold h, h x ==> Sum.inl (x, x) [Meta.Tactic.simp.rewrite] @eq_self:1000, x + x = x + x ==> True Try this: simp only [h, Nat.sub_add_cancel] [Meta.Tactic.simp.rewrite] h:1000, 1 ≤ x ==> True [Meta.Tactic.simp.rewrite] @Nat.sub_add_cancel:1000, x - 1 + 1 ==> x [Meta.Tactic.simp.rewrite] @eq_self:1000, x + 2 = x + 2 ==> True Try this: simp (config := { contextual := true }) only [Nat.sub_add_cancel] [Meta.Tactic.simp.rewrite] h:1000, 1 ≤ x ==> True [Meta.Tactic.simp.rewrite] @Nat.sub_add_cancel:1000, x - 1 + 1 ==> x [Meta.Tactic.simp.rewrite] @eq_self:1000, (if h : 1 ≤ x then x else 0) = if _h : 1 ≤ x then x else 0 ==> True Try this: simp only [and_self] [Meta.Tactic.simp.rewrite] and_self:1000, b ∧ b ==> b [Meta.Tactic.simp.rewrite] iff_self:1000, a ∧ b ↔ a ∧ b ==> True Try this: simp only [my_thm] [Meta.Tactic.simp.rewrite] @my_thm:1000, b ∧ b ==> b [Meta.Tactic.simp.rewrite] @eq_self:1000, (a ∧ b) = (a ∧ b) ==> True Try this: simp (discharger := sorry) only [Nat.sub_add_cancel] simp_trace.lean:85:0-85:7: warning: declaration uses 'sorry' [Meta.Tactic.simp.rewrite] @Nat.sub_add_cancel:1000, x - 1 + 1 ==> x [Meta.Tactic.simp.rewrite] @eq_self:1000, x = x ==> True Try this: simp only [bla, h] at * [Meta.Tactic.simp.rewrite] unfold bla, bla x ==> match h x with | Sum.inl (y, z) => y + z | Sum.inr val => 0 [Meta.Tactic.simp.rewrite] unfold h, h x ==> Sum.inl (x, x) Try this: simp only [bla, h] at h' [Meta.Tactic.simp.rewrite] unfold bla, bla x ==> match h x with | Sum.inl (y, z) => y + z | Sum.inr val => 0 [Meta.Tactic.simp.rewrite] unfold h, h x ==> Sum.inl (x, x) Try this: simp only [bla, h, List.length_append] at * simp_trace.lean:101:101-102:40: error: unsolved goals x y : Nat α : Type xs ys : List α h₁ : x + x = y h₂ : List.length xs + List.length ys = y ⊢ x = length xs [Meta.Tactic.simp.rewrite] unfold bla, bla x ==> match h x with | Sum.inl (y, z) => y + z | Sum.inr val => 0 [Meta.Tactic.simp.rewrite] unfold h, h x ==> Sum.inl (x, x) [Meta.Tactic.simp.rewrite] @List.length_append:1000, List.length (xs ++ ys) ==> List.length xs + List.length ys Try this: simp only [bla, h, List.length_append] at * simp_trace.lean:105:101-106:53: error: unsolved goals x y : Nat α : Type xs ys : List α h₁ : x + x = y h₂ : List.length xs + List.length ys = y ⊢ x = length xs [Meta.Tactic.simp.rewrite] unfold bla, bla x ==> match h x with | Sum.inl (y, z) => y + z | Sum.inr val => 0 [Meta.Tactic.simp.rewrite] unfold h, h x ==> Sum.inl (x, x) [Meta.Tactic.simp.rewrite] @List.length_append:1000, List.length (xs ++ ys) ==> List.length xs + List.length ys Try this: simp only [bla, h] at * [Meta.Tactic.simp.rewrite] unfold bla, bla x ==> match h x with | Sum.inl (y, z) => y + z | Sum.inr val => 0 [Meta.Tactic.simp.rewrite] unfold h, h x ==> Sum.inl (x, x) [Meta.Tactic.simp.rewrite] unfold bla, bla y ==> match h y with | Sum.inl (y, z) => y + z | Sum.inr val => 0 [Meta.Tactic.simp.rewrite] unfold h, h y ==> Sum.inl (y, y) Try this: simp only [bla, h] at * [Meta.Tactic.simp.rewrite] unfold bla, bla x ==> match h x with | Sum.inl (y, z) => y + z | Sum.inr val => 0 [Meta.Tactic.simp.rewrite] unfold h, h x ==> Sum.inl (x, x) [Meta.Tactic.simp.rewrite] unfold bla, bla x ==> match h x with | Sum.inl (y, z) => y + z | Sum.inr val => 0 [Meta.Tactic.simp.rewrite] unfold h, h x ==> Sum.inl (x, x) Try this: simp only [HasProp.toProp]