61186629d6
This PR implements the option `revert`, which is set to `false` by default. To recover the old `grind` behavior, you should use `grind +revert`. Previously, `grind` used the `RevSimpIntro` idiom, i.e., it would revert all hypotheses and then re-introduce them while simplifying and applying eager `cases`. This idiom created several problems: * Users reported that `grind` would include unnecessary parameters. See [here](https://leanprover.zulipchat.com/#narrow/channel/270676-lean4/topic/Grind.20aggressively.20includes.20local.20hypotheses.2E/near/554887715). * Unnecessary section variables were also being introduced. See the new test contributed by Sebastian Graf. * Finally, it prevented us from supporting arbitrary parameters as we do in `simp`. In `simp`, I implemented a mechanism that simulates local universe-polymorphic theorems, but this approach could not be used in `grind` because there is no mechanism for reverting (and re-introducing) local universe-polymorphic theorems. Adding such a mechanism would require substantial work: I would need to modify the local context object. I considered maintaining a substitution from the original variables to the new ones, but this is also tricky, because the mapping would have to be stored in the `grind` goal objects, and it is not just a simple mapping. After reverting everything, I would need to keep a sequence of original variables that must be added to the mapping as we re-introduce them, but eager case splits complicate this quite a bit. The whole approach felt overly messy. The new behavior `grind -revert` addresses all these issues. None of the `grind` proofs in our test suite broke after we fixed the bugs exposed by the new feature. That said, the traces and counterexamples produced by `grind` are different. The new proof terms are also different.
107 lines
2.3 KiB
Text
107 lines
2.3 KiB
Text
section Mathlib.Algebra.Group.Units.Defs
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variable {α : Type}
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structure Units (α : Type) [Mul α] [One α] where
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val : α
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inv : α
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val_inv : val * inv = 1
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inv_val : inv * val = 1
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postfix:1024 "ˣ" => Units
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instance [Mul α] [One α] : CoeHead αˣ α :=
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⟨Units.val⟩
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variable {M : Type} {N : Type}
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def IsUnit [Mul M] [One M] (a : M) : Prop := ∃ u : Mˣ, (u : M) = a
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theorem isUnit_iff_exists [Mul M] [One M] {x : M} : IsUnit x ↔ ∃ b, x * b = 1 ∧ b * x = 1 := sorry
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end Mathlib.Algebra.Group.Units.Defs
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section Mathlib.Algebra.GroupWithZero.Defs
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variable {M₀ : Type}
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variable [Mul M₀] [Zero M₀] {a b c : M₀}
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theorem mul_left_cancel₀ (ha : a ≠ 0) (h : a * b = a * c) : b = c := sorry
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theorem mul_right_cancel₀ (hb : b ≠ 0) (h : a * b = c * b) : a = c := sorry
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end Mathlib.Algebra.GroupWithZero.Defs
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section Mathlib.Algebra.Divisibility.Basic
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variable {α : Type} [Mul α]
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instance semigroupDvd : Dvd α :=
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Dvd.mk fun a b => ∃ c, b = a * c
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end Mathlib.Algebra.Divisibility.Basic
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section Mathlib.Algebra.Divisibility.Units
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variable {α : Type} [Mul α] [One α] {a b u : α}
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namespace IsUnit
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theorem dvd_mul_right (hu : IsUnit u) : a ∣ b * u ↔ a ∣ b := sorry
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theorem mul_right_dvd (hu : IsUnit u) : a * u ∣ b ↔ a ∣ b := sorry
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end IsUnit
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theorem isUnit_of_dvd_one {a : α} (h : a ∣ 1) : IsUnit (a : α) := sorry
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end Mathlib.Algebra.Divisibility.Units
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variable {α : Type} [Mul α] [One α] [Zero α]
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def DvdNotUnit (a b : α) : Prop :=
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a ≠ 0 ∧ ∃ x, ¬IsUnit x ∧ b = a * x
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/--
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error: `grind` failed
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case grind.1
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α : Type
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inst : Mul α
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inst_1 : One α
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inst_2 : Zero α
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x y : α
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h : DvdNotUnit x y
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hx0 : x ≠ 0
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d : α
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hdu : ¬IsUnit d
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hdx : y = x * d
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h_1 : y ∣ x
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e : α
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he : x = y * e
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h_2 : ¬x * 1 = x * (d * e)
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left : IsUnit e
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w : α
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left_1 : e * w = 1
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right_1 : w * e = 1
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w_1 : α
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left_2 : e * w_1 = 1
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right_2 : w_1 * e = 1
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⊢ False
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-/
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#guard_msgs in
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theorem dvd_and_not_dvd_iff {x y : α} :
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x ∣ y ∧ ¬y ∣ x ↔ DvdNotUnit x y :=
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⟨sorry,
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fun ⟨hx0, d, hdu, hdx⟩ =>
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⟨⟨d, hdx⟩, fun ⟨e, he⟩ =>
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hdu
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(isUnit_of_dvd_one
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⟨e, mul_left_cancel₀ hx0 <| by
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set_option trace.Meta.debug true in
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grind -verbose [
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isUnit_iff_exists,
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IsUnit.dvd_mul_right,
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IsUnit.mul_right_dvd
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]
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⟩)⟩⟩
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