0e49576fe4
This PR makes `#guard_msgs` to treat `trace` messages separate from `info`, `warning` and `error`. It also introduce the ability to say `#guard_msgs (pass info`, like `(drop info)` so far, and also adds `(check info)` as the explicit form of `(info)`, for completeness. Fixes #8266
101 lines
2.1 KiB
Text
101 lines
2.1 KiB
Text
def f (x y : Nat) : Nat :=
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match x, y with
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| 0, 0 => 1
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| 0, y => y
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| x+1, 5 => 2 * f x 0
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| x+1, y => 2 * f x y
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/--
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trace: x y : Nat
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h : y ≠ 5
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⊢ ∃ z, 2 * f x y = 2 * z
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-/
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#guard_msgs in
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theorem ex1 (x : Nat) (y : Nat) (h : y ≠ 5) : ∃ z, f (x+1) y = 2 * z := by
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simp [f, h]
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trace_state
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apply Exists.intro
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rfl
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@[simp] def g (x y : Nat) : Nat :=
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match x, y with
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| 0, 0 => 1
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| 0, y => y
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| x+1, 5 => 2 * g x 0
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| x+1, y => 2 * g x y
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/--
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trace: x y : Nat
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h : y ≠ 5
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⊢ ∃ z, 2 * g x y = 2 * z
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-/
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#guard_msgs in
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theorem ex2 (x : Nat) (y : Nat) (h : y ≠ 5) : ∃ z, g (x+1) y = 2 * z := by
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simp [h]
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trace_state
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apply Exists.intro
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rfl
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/--
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trace: x y : Nat
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h : y = 5 → False
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⊢ ∃ z, 2 * f x y = 2 * z
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-/
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#guard_msgs in
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theorem ex3 (x : Nat) (y : Nat) (h : y = 5 → False) : ∃ z, f (x+1) y = 2 * z := by
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simp [f, h]
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trace_state
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apply Exists.intro
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rfl
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@[simp] def f2 (x y z : Nat) : Nat :=
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match x, y, z with
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| 0, 0, 0 => 1
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| 0, y, z => y
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| x+1, 5, 6 => 2 * f2 x 0 1
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| x+1, y, z => 2 * f2 x y z
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#check f2.eq_4
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/--
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trace: x y z : Nat
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h : y = 5 → z = 6 → False
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⊢ ∃ w, 2 * f2 x y z = 2 * w
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-/
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#guard_msgs in
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theorem ex4 (x y z : Nat) (h : y = 5 → z = 6 → False) : ∃ w, f2 (x+1) y z = 2 * w := by
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simp [f2, h]
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trace_state
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apply Exists.intro
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rfl
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theorem ex5 (x y z : Nat) (h1 : y ≠ 5) : ∃ w, f2 (x+1) y z = 2 * w := by
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simp [f2, h1]
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apply Exists.intro
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rfl
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theorem ex6 (x y z : Nat) (h2 : z ≠ 6) : ∃ w, f2 (x+1) y z = 2 * w := by
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simp [f2, h2]
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apply Exists.intro
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rfl
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@[simp] def f3 (x y z : Nat) : Nat :=
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match x, y, z with
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| 0, 0, 0 => 1
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| 0, y, z => y
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| x+1, 5, 6 => 4 * f3 x 0 1
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| x+1, 6, 4 => 3 * f3 x 0 1
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| x+1, y, z => 2 * f3 x y z
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#check f3.eq_5
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theorem ex7 (x y z : Nat) (h2 : z ≠ 6) (h3 : y ≠ 6) : ∃ w, f3 (x+1) y z = 2 * w := by
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simp [f3, h2, h3]
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apply Exists.intro
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rfl
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theorem ex8 (x y z : Nat) (h2 : y = 5 → z = 6 → False) (h3 : y = 6 → z = 4 → False) : ∃ w, f3 (x+1) y z = 2 * w := by
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simp [f3, h2, h3]
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apply Exists.intro
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rfl
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