67 lines
1.8 KiB
Text
67 lines
1.8 KiB
Text
module
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set_option trace.grind.split true
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set_option trace.grind.eqc true
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example (p q : Prop) : p ∨ q → p ∨ ¬q → ¬p ∨ q → ¬p ∨ ¬q → False := by
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grind
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opaque R : Nat → Prop
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/--
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trace: [grind] working on goal `grind`
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[grind.eqc] (if p then a else b) = c
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[grind.eqc] R a = True
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[grind.eqc] R b = True
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[grind.eqc] R c = False
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[grind.split] if p then a else b, generation: 0
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[grind] working on goal `grind.1`
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[grind.eqc] p = True
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[grind.eqc] (if p then a else b) = a
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[grind.eqc] R a = R c
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[grind] closed `grind.1`
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[grind] working on goal `grind.2`
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[grind.eqc] p = False
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[grind.eqc] (if p then a else b) = b
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[grind.eqc] R b = R c
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[grind] closed `grind.2`
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-/
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#guard_msgs (trace) in
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set_option trace.grind true in
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example (p : Prop) [Decidable p] (a b c : Nat) : (if p then a else b) = c → R a → R b → R c := by
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grind
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example (p : Prop) [Decidable p] (a b c : Nat) : (if p then a else b) = c → R a → R b → R c := by
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fail_if_success grind (splitIte := false)
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sorry
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namespace grind_test_induct_pred
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inductive Expr where
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| nat : Nat → Expr
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| plus : Expr → Expr → Expr
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| bool : Bool → Expr
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| and : Expr → Expr → Expr
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deriving DecidableEq
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inductive Ty where
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| nat
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| bool
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deriving DecidableEq
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inductive HasType : Expr → Ty → Prop
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| nat : HasType (.nat v) .nat
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| plus : HasType a .nat → HasType b .nat → HasType (.plus a b) .nat
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| bool : HasType (.bool v) .bool
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| and : HasType a .bool → HasType b .bool → HasType (.and a b) .bool
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set_option trace.grind true
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theorem HasType.det (h₁ : HasType e t₁) (h₂ : HasType e t₂) : t₁ = t₂ := by
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grind [HasType]
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example (h₁ : HasType e t₁) (h₂ : HasType e t₂) : t₁ = t₂ := by
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grind +splitIndPred
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example (h₁ : HasType e t₁) (h₂ : HasType e t₂) : t₁ = t₂ := by
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fail_if_success grind
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sorry
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end grind_test_induct_pred
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