a062eea204
This PR adds support for beta reduction in the `grind` tactic. `grind` can now solve goals such as ```lean example (f : Nat → Nat) : f = (fun x : Nat => x + 5) → f 2 > 5 := by grind ```
72 lines
1.7 KiB
Text
72 lines
1.7 KiB
Text
def f (x : Nat) : Nat → Nat → Nat :=
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match x with
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| 0 => fun _ _ => 0
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| _+1 => fun a b => a + b
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example : f 0 b c = 0 := by
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grind [f]
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example : f (a+1) b c = b + c := by
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grind [f]
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example : f x b c ≠ b + c → x = a + 1 → False := by
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grind [f]
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example : x = a + 1 → f x b c ≠ b + c → False := by
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grind [f]
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example : x = a + 1 → f x b c ≠ b + c → False := by
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grind [f]
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example : f x b c > 0 → x = 0 → False := by
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grind [f]
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example : f x b c > 0 → x ≠ 0 := by
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grind [f]
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example (f : Nat → Nat → Nat) : f 2 3 ≠ 5 → f = (fun x y : Nat => x + y) → False := by
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grind
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opaque bla : Nat → Nat → Nat → Nat
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/--
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info: [grind.beta] f 2 3 = bla 2 3 2, using fun x y => bla x y x
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[grind.beta] f 2 3 = 2 + 3, using fun x y => x + y
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-/
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#guard_msgs (info) in
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set_option trace.grind.beta true in
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example (g h f : Nat → Nat → Nat) :
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f 2 3 ≠ 5 →
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g = (fun x y : Nat => x + y) →
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h = (fun x y => bla x y x) →
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g = h →
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f = h →
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False := by
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grind
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example (g h f : Nat → Nat → Nat) :
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f 2 3 ≠ 5 →
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h = (fun x y => bla x y x) →
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g = (fun x y : Nat => x + y) →
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g = h →
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h = f →
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False := by
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grind
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example (f : Nat → Nat → Nat) : f = (fun x y : Nat => x + y) → f 2 3 = 5 := by
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grind
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example (f g h : Nat → Nat → Nat) :
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h = (fun x y => bla x y x) →
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g = (fun x y : Nat => x + y) →
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g = h →
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h = f →
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f 2 3 = 5 := by
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grind
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example (f : Nat → Nat) : f = (fun x : Nat => x + 5) → f 2 > 5 := by
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grind
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example (f : Nat → Nat → Nat) : f a = (fun x : Nat => x + 5) → f a 2 > 5 := by
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grind
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