150 lines
4.3 KiB
Text
150 lines
4.3 KiB
Text
module
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opaque g : Nat → Nat
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@[simp] def f (a : Nat) :=
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match a with
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| 0 => 10
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| x+1 => g (f x)
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set_option trace.grind.ematch.pattern true
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set_option trace.grind.ematch.instance true
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set_option trace.grind.assert true
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/-- trace: [grind.ematch.pattern] f.eq_2: [f (#0 + 1)] -/
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#guard_msgs in
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grind_pattern f.eq_2 => f (x + 1)
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/--
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trace: [grind.assert] f (y + 1) = a
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[grind.assert] ¬a = g (f y)
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[grind.ematch.instance] f.eq_2: f y.succ = g (f y)
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[grind.assert] f (y + 1) = g (f y)
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-/
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#guard_msgs (trace) in
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example : f (y + 1) = a → a = g (f y) := by
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grind
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/--
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trace: [grind.assert] f 1 = a
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[grind.assert] ¬a = g (f 0)
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[grind.ematch.instance] f.eq_2: f (Nat.succ 0) = g (f 0)
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[grind.assert] f 1 = g (f 0)
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-/
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#guard_msgs (trace) in
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example : f 1 = a → a = g (f 0) := by
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grind
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/--
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trace: [grind.assert] f 10 = a
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[grind.assert] ¬a = g (f 9)
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[grind.ematch.instance] f.eq_2: f (Nat.succ 8) = g (f 8)
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[grind.ematch.instance] f.eq_2: f (Nat.succ 9) = g (f 9)
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[grind.assert] f 9 = g (f 8)
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[grind.assert] f 10 = g (f 9)
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-/
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#guard_msgs (trace) in
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example : f 10 = a → a = g (f 9) := by
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grind
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/--
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trace: [grind.assert] f (c + 2) = a
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[grind.assert] ¬a = g (g (f c))
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[grind.ematch.instance] f.eq_2: f (c + 1).succ = g (f (c + 1))
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[grind.assert] f (c + 2) = g (f (c + 1))
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[grind.ematch.instance] f.eq_2: f c.succ = g (f c)
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[grind.assert] f (c + 1) = g (f c)
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-/
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#guard_msgs (trace) in
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example : f (c + 2) = a → a = g (g (f c)) := by
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grind
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@[simp] def foo (a : Nat) :=
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match a with
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| 0 => 10
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| 1 => 10
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| a+2 => g (foo a)
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/-- trace: [grind.ematch.pattern] foo.eq_3: [foo (#0 + 2)] -/
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#guard_msgs in
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grind_pattern foo.eq_3 => foo (a_2 + 2)
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-- The instance is correctly found in the following example.
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-- TODO: to complete the proof, we need linear arithmetic support to prove that `b + 2 = c + 1`.
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/--
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trace: [grind.assert] foo (c + 1) = a
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[grind.assert] c = b + 1
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[grind.assert] ¬a = g (foo b)
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[grind.ematch.instance] foo.eq_3: foo b.succ.succ = g (foo b)
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[grind.assert] foo (b + 2) = g (foo b)
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-/
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#guard_msgs (trace) in
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example : foo (c + 1) = a → c = b + 1 → a = g (foo b) := by
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grind
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set_option trace.grind.assert false
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/--
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trace: [grind.ematch.instance] f.eq_2: f (x + 99).succ = g (f (x + 99))
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[grind.ematch.instance] f.eq_2: f (x + 98).succ = g (f (x + 98))
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-/
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#guard_msgs (trace) in
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example : f (x + 100) = a → a = b := by
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fail_if_success grind (ematch := 2)
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sorry
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/--
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trace: [grind.ematch.instance] f.eq_2: f (x + 99).succ = g (f (x + 99))
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[grind.ematch.instance] f.eq_2: f (x + 98).succ = g (f (x + 98))
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[grind.ematch.instance] f.eq_2: f (x + 97).succ = g (f (x + 97))
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[grind.ematch.instance] f.eq_2: f (x + 96).succ = g (f (x + 96))
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[grind.ematch.instance] f.eq_2: f (x + 95).succ = g (f (x + 95))
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-/
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#guard_msgs (trace) in
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example : f (x + 100) = a → a = b := by
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fail_if_success grind (ematch := 5)
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sorry
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/--
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trace: [grind.ematch.instance] f.eq_2: f (x + 99).succ = g (f (x + 99))
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[grind.ematch.instance] f.eq_2: f (x + 98).succ = g (f (x + 98))
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[grind.ematch.instance] f.eq_2: f (x + 97).succ = g (f (x + 97))
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[grind.ematch.instance] f.eq_2: f (x + 96).succ = g (f (x + 96))
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-/
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#guard_msgs (trace) in
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example : f (x + 100) = a → a = b := by
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fail_if_success grind (ematch := 100) (instances := 4)
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sorry
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/--
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trace: [grind.ematch.instance] f.eq_2: f (y + 9).succ = g (f (y + 9))
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[grind.ematch.instance] f.eq_2: f (x + 99).succ = g (f (x + 99))
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[grind.ematch.instance] f.eq_2: f (x + 98).succ = g (f (x + 98))
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[grind.ematch.instance] f.eq_2: f (y + 8).succ = g (f (y + 8))
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[grind.ematch.instance] f.eq_2: f (y + 7).succ = g (f (y + 7))
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-/
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#guard_msgs (trace) in
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example : f (x + 100) = a → f (y + 10) = c → a = b := by
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fail_if_success grind (ematch := 100) (instances := 5)
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sorry
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/--
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trace: [grind.ematch.instance] f.eq_2: f (x + 99).succ = g (f (x + 99))
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[grind.ematch.instance] f.eq_2: f (x + 98).succ = g (f (x + 98))
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-/
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#guard_msgs (trace) in
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example : f (x + 100) = a → a = b := by
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fail_if_success grind (gen := 2)
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sorry
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/--
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trace: [grind.ematch.instance] f.eq_2: f (x + 99).succ = g (f (x + 99))
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[grind.ematch.instance] f.eq_2: f (x + 98).succ = g (f (x + 98))
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[grind.ematch.instance] f.eq_2: f (x + 97).succ = g (f (x + 97))
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[grind.ematch.instance] f.eq_2: f (x + 96).succ = g (f (x + 96))
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[grind.ematch.instance] f.eq_2: f (x + 95).succ = g (f (x + 95))
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-/
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#guard_msgs (trace) in
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example : f (x + 100) = a → a = b := by
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fail_if_success grind (gen := 5)
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sorry
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