diff --git a/src/Init/Data/Array/DecidableEq.lean b/src/Init/Data/Array/DecidableEq.lean index 6afecd70d8..593840201d 100644 --- a/src/Init/Data/Array/DecidableEq.lean +++ b/src/Init/Data/Array/DecidableEq.lean @@ -11,13 +11,13 @@ namespace Array theorem eq_of_isEqvAux [DecidableEq α] (a b : Array α) (hsz : a.size = b.size) (i : Nat) (hi : i ≤ a.size) (heqv : Array.isEqvAux a b hsz (fun x y => x = y) i) (j : Nat) (low : i ≤ j) (high : j < a.size) : a.get ⟨j, high⟩ = b.get ⟨j, hsz ▸ high⟩ := by by_cases h : i < a.size - . unfold Array.isEqvAux at heqv + · unfold Array.isEqvAux at heqv simp [h] at heqv have hind := eq_of_isEqvAux a b hsz (i+1) (Nat.succ_le_of_lt h) heqv.2 by_cases heq : i = j - . subst heq; exact heqv.1 - . exact hind j (Nat.succ_le_of_lt (Nat.lt_of_le_and_ne low heq)) high - . have heq : i = a.size := Nat.le_antisymm hi (Nat.ge_of_not_lt h) + · subst heq; exact heqv.1 + · exact hind j (Nat.succ_le_of_lt (Nat.lt_of_le_and_ne low heq)) high + · have heq : i = a.size := Nat.le_antisymm hi (Nat.ge_of_not_lt h) subst heq exact absurd (Nat.lt_of_lt_of_le high low) (Nat.lt_irrefl j) termination_by _ => a.size - i diff --git a/src/Init/Data/Array/Mem.lean b/src/Init/Data/Array/Mem.lean index 6cad3386ac..b9d7ce7b74 100644 --- a/src/Init/Data/Array/Mem.lean +++ b/src/Init/Data/Array/Mem.lean @@ -33,10 +33,10 @@ theorem sizeOf_lt_of_mem [DecidableEq α] [SizeOf α] {as : Array α} (h : a ∈ let rec aux (j : Nat) (h : anyM.loop (m := Id) (fun b => decide (a = b)) as as.size (Nat.le_refl ..) j = true) : sizeOf a < sizeOf as := by unfold anyM.loop at h split at h - . simp [Bind.bind, pure] at h; split at h + · simp [Bind.bind, pure] at h; split at h next he => subst a; apply sizeOf_get_lt next => have ih := aux (j+1) h; assumption - . contradiction + · contradiction apply aux 0 h termination_by aux j _ => as.size - j diff --git a/src/Init/Data/Nat/Linear.lean b/src/Init/Data/Nat/Linear.lean index d447fcdebc..9cc081956a 100644 --- a/src/Init/Data/Nat/Linear.lean +++ b/src/Init/Data/Nat/Linear.lean @@ -356,26 +356,26 @@ theorem Poly.denote_eq_cancelAux (ctx : Context) (fuel : Nat) (m₁ m₂ r₁ r split <;> simp at h <;> try assumption rename_i k₁ v₁ m₁ k₂ v₂ m₂ by_cases hltv : Nat.blt v₁ v₂ <;> simp [hltv] - . apply ih; simp [denote_eq] at h |-; assumption - . by_cases hgtv : Nat.blt v₂ v₁ <;> simp [hgtv] - . apply ih; simp [denote_eq] at h |-; assumption - . have heqv : v₁ = v₂ := eq_of_not_blt_eq_true hltv hgtv; subst heqv + · apply ih; simp [denote_eq] at h |-; assumption + · by_cases hgtv : Nat.blt v₂ v₁ <;> simp [hgtv] + · apply ih; simp [denote_eq] at h |-; assumption + · have heqv : v₁ = v₂ := eq_of_not_blt_eq_true hltv hgtv; subst heqv by_cases hltk : Nat.blt k₁ k₂ <;> simp [hltk] - . apply ih + · apply ih simp [denote_eq] at h |- have haux : k₁ * Var.denote ctx v₁ ≤ k₂ * Var.denote ctx v₁ := Nat.mul_le_mul_right _ (Nat.le_of_lt (Nat.blt_eq.mp hltk)) rw [Nat.mul_sub_right_distrib, ← Nat.add_assoc, ← Nat.add_sub_assoc haux] apply Eq.symm apply Nat.sub_eq_of_eq_add simp [h] - . by_cases hgtk : Nat.blt k₂ k₁ <;> simp [hgtk] - . apply ih + · by_cases hgtk : Nat.blt k₂ k₁ <;> simp [hgtk] + · apply ih simp [denote_eq] at h |- have haux : k₂ * Var.denote ctx v₁ ≤ k₁ * Var.denote ctx v₁ := Nat.mul_le_mul_right _ (Nat.le_of_lt (Nat.blt_eq.mp hgtk)) rw [Nat.mul_sub_right_distrib, ← Nat.add_assoc, ← Nat.add_sub_assoc haux] apply Nat.sub_eq_of_eq_add simp [h] - . have heqk : k₁ = k₂ := eq_of_not_blt_eq_true hltk hgtk; subst heqk + · have heqk : k₁ = k₂ := eq_of_not_blt_eq_true hltk hgtk; subst heqk apply ih simp [denote_eq] at h |- rw [← Nat.add_assoc, ← Nat.add_assoc] at h @@ -390,25 +390,25 @@ theorem Poly.of_denote_eq_cancelAux (ctx : Context) (fuel : Nat) (m₁ m₂ r₁ split at h <;> simp <;> try assumption rename_i k₁ v₁ m₁ k₂ v₂ m₂ by_cases hltv : Nat.blt v₁ v₂ <;> simp [hltv] at h - . have ih := ih (h := h); simp [denote_eq] at ih ⊢; assumption - . by_cases hgtv : Nat.blt v₂ v₁ <;> simp [hgtv] at h - . have ih := ih (h := h); simp [denote_eq] at ih ⊢; assumption - . have heqv : v₁ = v₂ := eq_of_not_blt_eq_true hltv hgtv; subst heqv + · have ih := ih (h := h); simp [denote_eq] at ih ⊢; assumption + · by_cases hgtv : Nat.blt v₂ v₁ <;> simp [hgtv] at h + · have ih := ih (h := h); simp [denote_eq] at ih ⊢; assumption + · have heqv : v₁ = v₂ := eq_of_not_blt_eq_true hltv hgtv; subst heqv by_cases hltk : Nat.blt k₁ k₂ <;> simp [hltk] at h - . have ih := ih (h := h); simp [denote_eq] at ih ⊢ + · have ih := ih (h := h); simp [denote_eq] at ih ⊢ have haux : k₁ * Var.denote ctx v₁ ≤ k₂ * Var.denote ctx v₁ := Nat.mul_le_mul_right _ (Nat.le_of_lt (Nat.blt_eq.mp hltk)) rw [Nat.mul_sub_right_distrib, ← Nat.add_assoc, ← Nat.add_sub_assoc haux] at ih have ih := Nat.eq_add_of_sub_eq (Nat.le_trans haux (Nat.le_add_left ..)) ih.symm simp at ih rw [ih] - . by_cases hgtk : Nat.blt k₂ k₁ <;> simp [hgtk] at h - . have ih := ih (h := h); simp [denote_eq] at ih ⊢ + · by_cases hgtk : Nat.blt k₂ k₁ <;> simp [hgtk] at h + · have ih := ih (h := h); simp [denote_eq] at ih ⊢ have haux : k₂ * Var.denote ctx v₁ ≤ k₁ * Var.denote ctx v₁ := Nat.mul_le_mul_right _ (Nat.le_of_lt (Nat.blt_eq.mp hgtk)) rw [Nat.mul_sub_right_distrib, ← Nat.add_assoc, ← Nat.add_sub_assoc haux] at ih have ih := Nat.eq_add_of_sub_eq (Nat.le_trans haux (Nat.le_add_left ..)) ih simp at ih rw [ih] - . have heqk : k₁ = k₂ := eq_of_not_blt_eq_true hltk hgtk; subst heqk + · have heqk : k₁ = k₂ := eq_of_not_blt_eq_true hltk hgtk; subst heqk have ih := ih (h := h); simp [denote_eq] at ih ⊢ rw [← Nat.add_assoc, ih, Nat.add_assoc] @@ -435,25 +435,25 @@ theorem Poly.denote_le_cancelAux (ctx : Context) (fuel : Nat) (m₁ m₂ r₁ r split <;> simp at h <;> try assumption rename_i k₁ v₁ m₁ k₂ v₂ m₂ by_cases hltv : Nat.blt v₁ v₂ <;> simp [hltv] - . apply ih; simp [denote_le] at h |-; assumption - . by_cases hgtv : Nat.blt v₂ v₁ <;> simp [hgtv] - . apply ih; simp [denote_le] at h |-; assumption - . have heqv : v₁ = v₂ := eq_of_not_blt_eq_true hltv hgtv; subst heqv + · apply ih; simp [denote_le] at h |-; assumption + · by_cases hgtv : Nat.blt v₂ v₁ <;> simp [hgtv] + · apply ih; simp [denote_le] at h |-; assumption + · have heqv : v₁ = v₂ := eq_of_not_blt_eq_true hltv hgtv; subst heqv by_cases hltk : Nat.blt k₁ k₂ <;> simp [hltk] - . apply ih + · apply ih simp [denote_le] at h |- have haux : k₁ * Var.denote ctx v₁ ≤ k₂ * Var.denote ctx v₁ := Nat.mul_le_mul_right _ (Nat.le_of_lt (Nat.blt_eq.mp hltk)) rw [Nat.mul_sub_right_distrib, ← Nat.add_assoc, ← Nat.add_sub_assoc haux] apply Nat.le_sub_of_add_le simp [h] - . by_cases hgtk : Nat.blt k₂ k₁ <;> simp [hgtk] - . apply ih + · by_cases hgtk : Nat.blt k₂ k₁ <;> simp [hgtk] + · apply ih simp [denote_le] at h |- have haux : k₂ * Var.denote ctx v₁ ≤ k₁ * Var.denote ctx v₁ := Nat.mul_le_mul_right _ (Nat.le_of_lt (Nat.blt_eq.mp hgtk)) rw [Nat.mul_sub_right_distrib, ← Nat.add_assoc, ← Nat.add_sub_assoc haux] apply Nat.sub_le_of_le_add simp [h] - . have heqk : k₁ = k₂ := eq_of_not_blt_eq_true hltk hgtk; subst heqk + · have heqk : k₁ = k₂ := eq_of_not_blt_eq_true hltk hgtk; subst heqk apply ih simp [denote_le] at h |- rw [← Nat.add_assoc, ← Nat.add_assoc] at h @@ -469,25 +469,25 @@ theorem Poly.of_denote_le_cancelAux (ctx : Context) (fuel : Nat) (m₁ m₂ r₁ split at h <;> simp <;> try assumption rename_i k₁ v₁ m₁ k₂ v₂ m₂ by_cases hltv : Nat.blt v₁ v₂ <;> simp [hltv] at h - . have ih := ih (h := h); simp [denote_le] at ih ⊢; assumption - . by_cases hgtv : Nat.blt v₂ v₁ <;> simp [hgtv] at h - . have ih := ih (h := h); simp [denote_le] at ih ⊢; assumption - . have heqv : v₁ = v₂ := eq_of_not_blt_eq_true hltv hgtv; subst heqv + · have ih := ih (h := h); simp [denote_le] at ih ⊢; assumption + · by_cases hgtv : Nat.blt v₂ v₁ <;> simp [hgtv] at h + · have ih := ih (h := h); simp [denote_le] at ih ⊢; assumption + · have heqv : v₁ = v₂ := eq_of_not_blt_eq_true hltv hgtv; subst heqv by_cases hltk : Nat.blt k₁ k₂ <;> simp [hltk] at h - . have ih := ih (h := h); simp [denote_le] at ih ⊢ + · have ih := ih (h := h); simp [denote_le] at ih ⊢ have haux : k₁ * Var.denote ctx v₁ ≤ k₂ * Var.denote ctx v₁ := Nat.mul_le_mul_right _ (Nat.le_of_lt (Nat.blt_eq.mp hltk)) rw [Nat.mul_sub_right_distrib, ← Nat.add_assoc, ← Nat.add_sub_assoc haux] at ih have := Nat.add_le_of_le_sub (Nat.le_trans haux (Nat.le_add_left ..)) ih simp at this exact this - . by_cases hgtk : Nat.blt k₂ k₁ <;> simp [hgtk] at h - . have ih := ih (h := h); simp [denote_le] at ih ⊢ + · by_cases hgtk : Nat.blt k₂ k₁ <;> simp [hgtk] at h + · have ih := ih (h := h); simp [denote_le] at ih ⊢ have haux : k₂ * Var.denote ctx v₁ ≤ k₁ * Var.denote ctx v₁ := Nat.mul_le_mul_right _ (Nat.le_of_lt (Nat.blt_eq.mp hgtk)) rw [Nat.mul_sub_right_distrib, ← Nat.add_assoc, ← Nat.add_sub_assoc haux] at ih have := Nat.le_add_of_sub_le ih simp at this exact this - . have heqk : k₁ = k₂ := eq_of_not_blt_eq_true hltk hgtk; subst heqk + · have heqk : k₁ = k₂ := eq_of_not_blt_eq_true hltk hgtk; subst heqk have ih := ih (h := h); simp [denote_le] at ih ⊢ have := Nat.add_le_add_right ih (k₁ * Var.denote ctx v₁) simp at this @@ -560,8 +560,8 @@ theorem ExprCnstr.denote_toPoly (ctx : Context) (c : ExprCnstr) : c.toPoly.denot cases c; rename_i eq lhs rhs simp [ExprCnstr.denote, PolyCnstr.denote, ExprCnstr.toPoly]; by_cases h : eq = true <;> simp [h] - . simp [Poly.denote_eq, Expr.toPoly] - . simp [Poly.denote_le, Expr.toPoly] + · simp [Poly.denote_eq, Expr.toPoly] + · simp [Poly.denote_le, Expr.toPoly] attribute [local simp] ExprCnstr.denote_toPoly @@ -569,8 +569,8 @@ theorem ExprCnstr.denote_toNormPoly (ctx : Context) (c : ExprCnstr) : c.toNormPo cases c; rename_i eq lhs rhs simp [ExprCnstr.denote, PolyCnstr.denote, ExprCnstr.toNormPoly] by_cases h : eq = true <;> simp [h] - . rw [Poly.denote_eq_cancel_eq]; simp [Poly.denote_eq, Expr.toNormPoly, Poly.norm] - . rw [Poly.denote_le_cancel_eq]; simp [Poly.denote_le, Expr.toNormPoly, Poly.norm] + · rw [Poly.denote_eq_cancel_eq]; simp [Poly.denote_eq, Expr.toNormPoly, Poly.norm] + · rw [Poly.denote_le_cancel_eq]; simp [Poly.denote_le, Expr.toNormPoly, Poly.norm] attribute [local simp] ExprCnstr.denote_toNormPoly @@ -593,10 +593,10 @@ theorem PolyCnstr.denote_mul (ctx : Context) (k : Nat) (c : PolyCnstr) : (c.mul have : (1 == 1) = true := rfl by_cases he : eq = true <;> simp [he, PolyCnstr.mul, PolyCnstr.denote, Poly.denote_le, Poly.denote_eq] <;> by_cases hk : k == 0 <;> (try simp [eq_of_beq hk]) <;> simp [*] <;> apply propext <;> apply Iff.intro <;> intro h - . exact Nat.eq_of_mul_eq_mul_left (Nat.zero_lt_succ _) h - . rw [h] - . exact Nat.le_of_mul_le_mul_left h (Nat.zero_lt_succ _) - . apply Nat.mul_le_mul_left _ h + · exact Nat.eq_of_mul_eq_mul_left (Nat.zero_lt_succ _) h + · rw [h] + · exact Nat.le_of_mul_le_mul_left h (Nat.zero_lt_succ _) + · apply Nat.mul_le_mul_left _ h end @@ -607,10 +607,10 @@ theorem PolyCnstr.denote_combine {ctx : Context} {c₁ c₂ : PolyCnstr} (h₁ : simp [denote] at h₁ h₂ simp [PolyCnstr.combine, denote] by_cases he₁ : eq₁ = true <;> by_cases he₂ : eq₂ = true <;> simp [he₁, he₂] at h₁ h₂ |- - . rw [Poly.denote_eq_cancel_eq]; simp [Poly.denote_eq] at h₁ h₂ |-; simp [h₁, h₂] - . rw [Poly.denote_le_cancel_eq]; simp [Poly.denote_eq, Poly.denote_le] at h₁ h₂ |-; rw [h₁]; apply Nat.add_le_add_left h₂ - . rw [Poly.denote_le_cancel_eq]; simp [Poly.denote_eq, Poly.denote_le] at h₁ h₂ |-; rw [h₂]; apply Nat.add_le_add_right h₁ - . rw [Poly.denote_le_cancel_eq]; simp [Poly.denote_eq, Poly.denote_le] at h₁ h₂ |-; apply Nat.add_le_add h₁ h₂ + · rw [Poly.denote_eq_cancel_eq]; simp [Poly.denote_eq] at h₁ h₂ |-; simp [h₁, h₂] + · rw [Poly.denote_le_cancel_eq]; simp [Poly.denote_eq, Poly.denote_le] at h₁ h₂ |-; rw [h₁]; apply Nat.add_le_add_left h₂ + · rw [Poly.denote_le_cancel_eq]; simp [Poly.denote_eq, Poly.denote_le] at h₁ h₂ |-; rw [h₂]; apply Nat.add_le_add_right h₁ + · rw [Poly.denote_le_cancel_eq]; simp [Poly.denote_eq, Poly.denote_le] at h₁ h₂ |-; apply Nat.add_le_add h₁ h₂ attribute [local simp] PolyCnstr.denote_combine @@ -624,26 +624,26 @@ theorem Poly.isNum?_eq_some (ctx : Context) {p : Poly} {k : Nat} : p.isNum? = so theorem Poly.of_isZero (ctx : Context) {p : Poly} (h : isZero p = true) : p.denote ctx = 0 := by simp [isZero] at h split at h - . simp - . contradiction + · simp + · contradiction theorem Poly.of_isNonZero (ctx : Context) {p : Poly} (h : isNonZero p = true) : p.denote ctx > 0 := by match p with | [] => contradiction | (k, v) :: p => by_cases he : v == fixedVar <;> simp [he, isNonZero] at h ⊢ - . simp [eq_of_beq he, Var.denote]; apply Nat.lt_of_succ_le; exact Nat.le_trans h (Nat.le_add_right ..) - . have ih := of_isNonZero ctx h + · simp [eq_of_beq he, Var.denote]; apply Nat.lt_of_succ_le; exact Nat.le_trans h (Nat.le_add_right ..) + · have ih := of_isNonZero ctx h exact Nat.le_trans ih (Nat.le_add_right ..) theorem PolyCnstr.eq_false_of_isUnsat (ctx : Context) {c : PolyCnstr} : c.isUnsat → c.denote ctx = False := by cases c; rename_i eq lhs rhs simp [isUnsat] by_cases he : eq = true <;> simp [he, denote, Poly.denote_eq, Poly.denote_le] - . intro + · intro | Or.inl ⟨h₁, h₂⟩ => simp [Poly.of_isZero, h₁]; have := Nat.not_eq_zero_of_lt (Poly.of_isNonZero ctx h₂); simp [this.symm] | Or.inr ⟨h₁, h₂⟩ => simp [Poly.of_isZero, h₂]; have := Nat.not_eq_zero_of_lt (Poly.of_isNonZero ctx h₁); simp [this] - . intro ⟨h₁, h₂⟩ + · intro ⟨h₁, h₂⟩ simp [Poly.of_isZero, h₂] have := Nat.not_le_of_gt (Poly.of_isNonZero ctx h₁) simp [this] @@ -652,9 +652,9 @@ theorem PolyCnstr.eq_true_of_isValid (ctx : Context) {c : PolyCnstr} : c.isValid cases c; rename_i eq lhs rhs simp [isValid] by_cases he : eq = true <;> simp [he, denote, Poly.denote_eq, Poly.denote_le] - . intro ⟨h₁, h₂⟩ + · intro ⟨h₁, h₂⟩ simp [Poly.of_isZero, h₁, h₂] - . intro h + · intro h simp [Poly.of_isZero, h] have := Nat.zero_le (Poly.denote ctx rhs) simp [this] @@ -696,8 +696,8 @@ theorem Certificate.of_combine_isUnsat (ctx : Context) (cs : Certificate) (h : c theorem denote_monomialToExpr (ctx : Context) (k : Nat) (v : Var) : (monomialToExpr k v).denote ctx = k * v.denote ctx := by simp [monomialToExpr] by_cases h : v == fixedVar <;> simp [h, Expr.denote] - . simp [eq_of_beq h, Var.denote] - . by_cases h : k == 1 <;> simp [h, Expr.denote]; simp [eq_of_beq h] + · simp [eq_of_beq h, Var.denote] + · by_cases h : k == 1 <;> simp [h, Expr.denote]; simp [eq_of_beq h] attribute [local simp] denote_monomialToExpr diff --git a/tests/lean/run/1024.lean b/tests/lean/run/1024.lean index b00887c6f5..25ed557243 100644 --- a/tests/lean/run/1024.lean +++ b/tests/lean/run/1024.lean @@ -16,14 +16,14 @@ namespace Vector (v.snoc x).nth k = x := by cases k; rename_i k hk induction v generalizing k <;> subst h - . simp only [nth] - . simp_all[nth] + · simp only [nth] + · simp_all[nth] theorem nth_snoc_eq_works (k: Fin (n+1))(v : Vector α n) (h: k.val = n): (v.snoc x).nth k = x := by cases k; rename_i k hk induction v generalizing k <;> subst h - . simp only [nth] - . simp[*,nth] + · simp only [nth] + · simp[*,nth] end Vector diff --git a/tests/lean/run/1025.lean b/tests/lean/run/1025.lean index 3f9c637971..238cdce884 100644 --- a/tests/lean/run/1025.lean +++ b/tests/lean/run/1025.lean @@ -15,6 +15,6 @@ namespace Vector (h: v.mem y): f y ≤ v.foldr (λ x acc => max (f x) acc) init := by induction v <;> simp only[foldr,max] - . admit - . split <;> admit + · admit + · split <;> admit end Vector diff --git a/tests/lean/run/501.lean b/tests/lean/run/501.lean index 9e02d49d7e..c2e68857b3 100644 --- a/tests/lean/run/501.lean +++ b/tests/lean/run/501.lean @@ -26,5 +26,5 @@ theorem pow_nonneg : ∀ m : Nat, 0 ^ m ≥ 0 | 0 => by decide | m@(_+1) => by rw [zeropow] - . decide - . apply Nat.zero_lt_succ + · decide + · apply Nat.zero_lt_succ diff --git a/tests/lean/run/860.lean b/tests/lean/run/860.lean index 7185b8c4e8..f19f89173f 100644 --- a/tests/lean/run/860.lean +++ b/tests/lean/run/860.lean @@ -6,11 +6,11 @@ private theorem pack_loop_terminates : (n : Nat) → n / 2 < n.succ | n+2 => by rw [Nat.div_eq] split - . rw [Nat.add_sub_self_right] + · rw [Nat.add_sub_self_right] have := pack_loop_terminates n calc n/2 + 1 < Nat.succ n + 1 := Nat.add_le_add_right this 1 _ < Nat.succ (n + 2) := Nat.succ_lt_succ (Nat.succ_lt_succ (Nat.lt_succ_self _)) - . apply Nat.zero_lt_succ + · apply Nat.zero_lt_succ def pack (n: Nat) : List Nat := let rec loop (n : Nat) (acc : Nat) (accs: List Nat) : List Nat := diff --git a/tests/lean/run/def10.lean b/tests/lean/run/def10.lean index 48f2d92654..a91dff8191 100644 --- a/tests/lean/run/def10.lean +++ b/tests/lean/run/def10.lean @@ -19,8 +19,8 @@ theorem ex5 : g false true true = 3 := rfl theorem f_eq (h : a = true → b = true → False) : f a b = 3 := by simp [f] split - . contradiction - . rfl + · contradiction + · rfl theorem ex6 : g x y z > 0 := by simp [g] diff --git a/tests/lean/run/eqThm.lean b/tests/lean/run/eqThm.lean index 7ef40eb157..a6aa20d52f 100644 --- a/tests/lean/run/eqThm.lean +++ b/tests/lean/run/eqThm.lean @@ -37,9 +37,9 @@ def foo (xs : List Nat) : List Nat := theorem foo_main_eq (xs : List Nat) : foo xs = foo.match_1 (fun _ => List Nat) xs (fun _ => []) (fun x xs => let y := 2*x; foo.match_1 (fun _ => List Nat) xs (fun _ => []) (fun x xs => (y + x)::foo xs)) := by split - . rfl - . split - . rfl - . rfl + · rfl + · split + · rfl + · rfl #check @foo_main_eq diff --git a/tests/lean/run/overAndPartialAppsAtWF.lean b/tests/lean/run/overAndPartialAppsAtWF.lean index c7e4b79dec..62281b3b2f 100644 --- a/tests/lean/run/overAndPartialAppsAtWF.lean +++ b/tests/lean/run/overAndPartialAppsAtWF.lean @@ -1,13 +1,13 @@ theorem eq_of_isEqvAux [DecidableEq α] (a b : Array α) (hsz : a.size = b.size) (i : Nat) (hi : i ≤ a.size) (heqv : Array.isEqvAux a b hsz (fun x y => x = y) i) : ∀ (j : Nat) (hl : i ≤ j) (hj : j < a.size), a.get ⟨j, hj⟩ = b.get ⟨j, hsz ▸ hj⟩ := by intro j low high by_cases h : i < a.size - . unfold Array.isEqvAux at heqv + · unfold Array.isEqvAux at heqv simp [h] at heqv have hind := eq_of_isEqvAux a b hsz (i+1) (Nat.succ_le_of_lt h) heqv.2 by_cases heq : i = j - . subst heq; exact heqv.1 - . exact hind j (Nat.succ_le_of_lt (Nat.lt_of_le_and_ne low heq)) high - . have heq : i = a.size := Nat.le_antisymm hi (Nat.ge_of_not_lt h) + · subst heq; exact heqv.1 + · exact hind j (Nat.succ_le_of_lt (Nat.lt_of_le_and_ne low heq)) high + · have heq : i = a.size := Nat.le_antisymm hi (Nat.ge_of_not_lt h) subst heq exact absurd (Nat.lt_of_lt_of_le high low) (Nat.lt_irrefl j) termination_by _ => a.size - i diff --git a/tests/lean/run/specialize2.lean b/tests/lean/run/specialize2.lean index 8024199996..55b62870eb 100644 --- a/tests/lean/run/specialize2.lean +++ b/tests/lean/run/specialize2.lean @@ -1,11 +1,11 @@ example : (p → q → False) ↔ (¬ p ∨ ¬ q) := by apply Iff.intro - . intro h + · intro h by_cases hp:p <;> by_cases hq:q - . specialize h hp hq; contradiction - . exact Or.inr hq - . exact Or.inl hp - . exact Or.inr hq - . intro + · specialize h hp hq; contradiction + · exact Or.inr hq + · exact Or.inl hp + · exact Or.inr hq + · intro | Or.inl hnp => intros; contradiction | Or.inr hnq => intros; contradiction diff --git a/tests/lean/run/split2.lean b/tests/lean/run/split2.lean index 5f4de57ba2..434a655f8f 100644 --- a/tests/lean/run/split2.lean +++ b/tests/lean/run/split2.lean @@ -9,19 +9,19 @@ example (x y z : Nat) : x ≠ 5 → y ≠ 5 → z ≠ 5 → f x y z = 1 := by intros simp [f] split - . contradiction - . contradiction - . contradiction - . rfl + · contradiction + · contradiction + · contradiction + · rfl example (x y z : Nat) : f x y z = y ∨ f x y z = 1 := by intros simp [f] split - . exact Or.inl rfl - . exact Or.inl rfl - . exact Or.inl rfl - . exact Or.inr rfl + · exact Or.inl rfl + · exact Or.inl rfl + · exact Or.inl rfl + · exact Or.inr rfl example (x y z : Nat) : f x y z = y ∨ f x y z = 1 := by intros diff --git a/tests/lean/run/split3.lean b/tests/lean/run/split3.lean index 1dfb00be9e..7a1da30984 100644 --- a/tests/lean/run/split3.lean +++ b/tests/lean/run/split3.lean @@ -17,8 +17,8 @@ example (a b : Bool) (x y z : Nat) (xs : List Nat) (h1 : (if a then x else y) = example (a : Bool) (h1 : (if a then x else y) = 1) : x + y > 0 := by split at h1 - . subst h1; rw [Nat.succ_add]; apply Nat.zero_lt_succ - . subst h1; apply Nat.zero_lt_succ + · subst h1; rw [Nat.succ_add]; apply Nat.zero_lt_succ + · subst h1; apply Nat.zero_lt_succ def f (x : Nat) : Nat := match x with @@ -29,9 +29,9 @@ def f (x : Nat) : Nat := example (h1 : f x = 0) (h2 : x > 300) : False := by simp [f] at h1 split at h1 - . contradiction - . contradiction - . contradiction + · contradiction + · contradiction + · contradiction example (h1 : f x = 0) (h2 : x > 300) : False := by simp [f] at h1 diff --git a/tests/lean/run/tactic1.lean b/tests/lean/run/tactic1.lean index 3785e5945a..8f3ed2fbed 100644 --- a/tests/lean/run/tactic1.lean +++ b/tests/lean/run/tactic1.lean @@ -61,9 +61,9 @@ example (x y z : Nat) (h₁ : x = y) (h₂ : z = y) : x = z := by example (x y z : Nat) (h₁ : x = y) (h₂ : z = y) : x = z := by apply Eq.trans - . sorry - . sorry - . sorry + · sorry + · sorry + · sorry example (x y z : Nat) (h₁ : x = y) (h₂ : z = y) : x = z := by apply Eq.trans <;> sorry diff --git a/tests/lean/run/wfOverapplicationIssue.lean b/tests/lean/run/wfOverapplicationIssue.lean index 4522ed8e60..fcc2cd14d3 100644 --- a/tests/lean/run/wfOverapplicationIssue.lean +++ b/tests/lean/run/wfOverapplicationIssue.lean @@ -4,9 +4,9 @@ theorem Array.sizeOf_lt_of_mem' [DecidableEq α] [SizeOf α] {as : Array α} (h unfold anyM.loop intro h split at h - . simp [Bind.bind, pure] at h; split at h + · simp [Bind.bind, pure] at h; split at h next he => subst a; apply sizeOf_get_lt next => have ih := aux (j+1) h; assumption - . contradiction + · contradiction apply aux 0 h termination_by aux j => as.size - j diff --git a/tests/lean/tacUnsolvedGoalsErrors.lean b/tests/lean/tacUnsolvedGoalsErrors.lean index ffc8605f23..54644d28f6 100644 --- a/tests/lean/tacUnsolvedGoalsErrors.lean +++ b/tests/lean/tacUnsolvedGoalsErrors.lean @@ -23,7 +23,7 @@ theorem ex4 (p q r : Prop) (h1 : p ∨ q) (h2 : p → q) : q := by theorem ex5 (p q r : Prop) (h1 : p ∨ q) (h2 : p → q) : q := by cases h1 - . skip -- Error here + · skip -- Error here skip - . skip -- Error here + · skip -- Error here skip