2f4340f63c
Now `refine stx` reports an error when there are natural unassigned metavariables after we elaborate syntax `stx`. The idea is that only synthetic holes `?<hole-name>` become new goals. The tactic `refine! stx` implements the Lean3 behavior.
99 lines
2.3 KiB
Text
99 lines
2.3 KiB
Text
@[recursor 4]
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def Or.elim2 {p q r : Prop} (major : p ∨ q) (left : p → r) (right : q → r) : r :=
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Or.elim major left right
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new_frontend
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theorem tst0 {p q : Prop } (h : p ∨ q) : q ∨ p :=
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by {
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induction h;
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{ apply Or.inr; assumption };
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{ apply Or.inl; assumption }
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}
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theorem tst1 {p q : Prop } (h : p ∨ q) : q ∨ p :=
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by {
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induction h with
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| inr h2 => exact Or.inl h2
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| inl h1 => exact Or.inr h1
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}
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theorem tst2 {p q : Prop } (h : p ∨ q) : q ∨ p :=
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by {
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induction h using elim2 with
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| left _ => { apply Or.inr; assumption }
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| right _ => { apply Or.inl; assumption }
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}
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theorem tst3 {p q : Prop } (h : p ∨ q) : q ∨ p :=
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by {
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induction h using elim2 with
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| right h => exact Or.inl h
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| left h => exact Or.inr h
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}
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theorem tst4 {p q : Prop } (h : p ∨ q) : q ∨ p :=
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by {
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induction h using elim2 with
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| right h => ?myright
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| left h => ?myleft;
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case myleft { exact Or.inr h };
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case myright { exact Or.inl h };
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}
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theorem tst5 {p q : Prop } (h : p ∨ q) : q ∨ p :=
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by {
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induction h using elim2 with
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| right h => _
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| left h => { refine Or.inr ?_; exact h };
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case right { exact Or.inl h }
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}
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theorem tst6 {p q : Prop } (h : p ∨ q) : q ∨ p :=
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by {
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cases h with
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| inr h2 => exact Or.inl h2
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| inl h1 => exact Or.inr h1
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}
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theorem tst7 {α : Type} (xs : List α) (h : (a : α) → (as : List α) → xs ≠ a :: as) : xs = [] :=
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by {
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induction xs with
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| nil => exact rfl
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| cons z zs ih => exact absurd rfl (h z zs)
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}
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theorem tst8 {α : Type} (xs : List α) (h : (a : α) → (as : List α) → xs ≠ a :: as) : xs = [] :=
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by {
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induction xs;
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exact rfl;
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exact absurd rfl $ h _ _
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}
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theorem tst9 {α : Type} (xs : List α) (h : (a : α) → (as : List α) → xs ≠ a :: as) : xs = [] :=
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by {
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cases xs with
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| nil => exact rfl
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| cons z zs => exact absurd rfl (h z zs)
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}
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theorem tst10 {p q : Prop } (h₁ : p ↔ q) (h₂ : p) : q :=
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by {
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induction h₁ using Iff.elim with
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| _ h _ => exact h h₂
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}
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def Iff2 (m p q : Prop) := p ↔ q
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theorem tst11 {p q r : Prop } (h₁ : Iff2 r p q) (h₂ : p) : q :=
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by {
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induction h₁ using Iff.elim with
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| _ h _ => exact h h₂
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}
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theorem tst12 {p q : Prop } (h₁ : p ∨ q) (h₂ : p ↔ q) (h₃ : p) : q :=
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by {
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failIfSuccess (induction h₁ using Iff.elim);
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induction h₂ using Iff.elim with
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| _ h _ => exact h h₃
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}
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