ab26eaf647
This PR is part 2 of the `implicit_reducible` refactoring (part 1: #12567). **Background.** When Lean checks definitional equality of function applications `f a₁ ... aₙ =?= f b₁ ... bₙ`, it compares arguments `aᵢ =?= bᵢ` at a transparency level determined by the binder type. Previously, only instance-implicit (`[C]`) arguments received a transparency bump to `.instances`. With `backward.isDefEq.implicitBump` enabled, ALL implicit arguments (`{x}`, `⦃x⦄`, and `[x]`) are bumped to `.instances`, so that definitions marked `[implicit_reducible]` unfold when comparing implicit arguments. This is important because implicit arguments often carry type information (e.g., `P (i + 0)` vs `P i`) where the mismatch is in non-proof positions (Sort arguments to `cast`) — proof irrelevance does not help here, so the relevant definitions must actually unfold. **`[implicit_reducible]`** (renamed from `[instance_reducible]` in part 1) marks definitions that should unfold at `TransparencyMode.instances` — between `[reducible]` (unfolds at `.reducible` and above) and the default `[semireducible]` (unfolds only at `.default` and above). This is the right level for core arithmetic operations that appear in type indices. ## Changes - **Enable `backward.isDefEq.implicitBump` by default** and set it in `stage0/src/stdlib_flags.h` so stage0 also compiles with it - **Mark `Nat.add`, `Nat.mul`, `Nat.sub`, `Array.size` as `[implicit_reducible]`** so they unfold when comparing implicit arguments at `.instances` transparency - **Remove redundant unification hints** (`n + 0 =?= n`, `n - 0 =?= n`, `n * 0 =?= 0`) that are now handled by `[implicit_reducible]` - **Rename all remaining `[instance_reducible]` attribute usages** to `[implicit_reducible]` across the codebase (the old name remains as an alias) - **Remove 28 `set_option backward.isDefEq.respectTransparency false in`** workarounds that are no longer needed 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> --------- Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>
46 lines
1.4 KiB
Text
46 lines
1.4 KiB
Text
structure PreInt where
|
|
minuend : Nat
|
|
subtrahend : Nat
|
|
|
|
/-- Definition 4.1.1 -/
|
|
instance PreInt.instSetoid : Setoid PreInt where
|
|
r a b := a.minuend + b.subtrahend = b.minuend + a.subtrahend
|
|
iseqv := {
|
|
refl := by grind
|
|
symm := by grind
|
|
trans := by grind
|
|
}
|
|
|
|
abbrev MyInt := Quotient PreInt.instSetoid
|
|
|
|
abbrev MyInt.formalDiff (a b : Nat) : MyInt := Quotient.mk PreInt.instSetoid ⟨ a, b ⟩
|
|
|
|
theorem MyInt.eq (a b c d : Nat) : formalDiff a b = formalDiff c d ↔ a + d = c + b :=
|
|
⟨ Quotient.exact, by intro h; exact Quotient.sound h ⟩
|
|
|
|
instance MyInt.instOfNat {n : Nat} : OfNat MyInt n where
|
|
ofNat := formalDiff n 0
|
|
|
|
instance MyInt.instNatCast : NatCast MyInt where
|
|
natCast n := formalDiff n 0
|
|
|
|
theorem MyInt.natCast_eq (n : Nat) : (n : MyInt) = formalDiff n 0 := rfl
|
|
|
|
theorem MyInt.natCast_inj (n m : Nat) :
|
|
(n : MyInt) = (m : MyInt) ↔ n = m := by
|
|
rw [natCast_eq, natCast_eq, eq]; simp
|
|
|
|
example (n m : Nat) : (n : MyInt) = (m : MyInt) ↔ n = m := by
|
|
grind [MyInt.natCast_eq, MyInt.eq]
|
|
|
|
@[grind]
|
|
theorem MyInt.eq_0_of_cast_eq_0 (n : Nat) (h : (n : MyInt) = 0) : n = 0 := by
|
|
rw [show (0 : MyInt) = ((0 : Nat) : MyInt) by rfl] at h
|
|
rwa [natCast_inj] at h
|
|
|
|
theorem MyInt.pos_iff_gt_0 {a : MyInt} : (∃ (n:Nat), n > 0 ∧ a = n) → a ≠ 0 := by
|
|
intro ⟨ w, hw ⟩ h
|
|
grind
|
|
|
|
example {a : MyInt} : (∃ (n:Nat), n > 0 ∧ a = n) → a ≠ 0 := by
|
|
grind
|