e1d15946f7
This PR enables the elaboration of theorem bodies, i.e. proofs, to happen in parallel to each other as well as to other elaboration tasks. Specifically, to be eligible for parallel proof elaboration, * the theorem must not be in a `mutual` block * `deprecated.oldSectionVars` must not be set * `Elab.async` must be set (currently defaults to `true` in the language server, `false` on the cmdline) To be activated for downstream projects (i.e. in stage 1) pending further Mathlib validation.
95 lines
2.1 KiB
Text
95 lines
2.1 KiB
Text
/-!
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# `decide +kernel` tests
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-/
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/-!
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Very basic tests
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-/
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theorem foo1 : True := by decide
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theorem foo2 : True := by decide +kernel
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/-!
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Tests of the error message when goal is false.
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-/
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/--
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error: tactic 'decide' proved that the proposition
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False
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is false
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-/
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#guard_msgs in
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theorem foo3 : False := by decide
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/--
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error: tactic 'decide' proved that the proposition
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False
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is false
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-/
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#guard_msgs in
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theorem foo4 : False := by decide +kernel
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/-!
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The kernel sees through irreducible definitions
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-/
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@[irreducible] def irred {α : Type} (x : α) : α := x
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/--
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error: tactic 'decide' failed for proposition
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irred 3 = 3
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since its 'Decidable' instance
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instDecidableEqNat (irred 3) 3
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did not reduce to 'isTrue' or 'isFalse'.
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After unfolding the instances 'instDecidableEqNat' and 'Nat.decEq', reduction got stuck at the 'Decidable' instance
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match h : (irred 3).beq 3 with
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| true => isTrue ⋯
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| false => isFalse ⋯
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-/
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#guard_msgs in theorem gcd_eq1 : irred 3 = 3 := by decide
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theorem gcd_eq2 : irred 3 = 3 := by decide +kernel
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/-!
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The proofs from `decide +kernel` are cached.
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-/
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theorem thm1 : ∀ x < 100, x * x ≤ 10000 := by decide +kernel
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theorem thm1' : ∀ x < 100, x * x ≤ 10000 := by decide +kernel
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/--
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info: theorem thm1 : ∀ (x : Nat), x < 100 → x * x ≤ 10000 :=
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thm1._auxLemma.1
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-/
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#guard_msgs in #print thm1
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/--
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info: theorem thm1' : ∀ (x : Nat), x < 100 → x * x ≤ 10000 :=
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thm1'._auxLemma.1
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-/
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#guard_msgs in #print thm1'
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/-!
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Reverting free variables.
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-/
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/--
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error: expected type must not contain free variables
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x + 1 ≤ 5
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Use the '+revert' option to automatically cleanup and revert free variables.
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-/
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#guard_msgs in
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example (x : Nat) (h : x < 5) : x + 1 ≤ 5 := by decide +kernel
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example (x : Nat) (h : x < 5) : x + 1 ≤ 5 := by decide +kernel +revert
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/--
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Can handle universe levels.
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-/
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instance (p : PUnit.{u} → Prop) [Decidable (p PUnit.unit)] : Decidable (∀ x : PUnit.{u}, p x) :=
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decidable_of_iff (p PUnit.unit) (by constructor; rintro _ ⟨⟩; assumption; intro h; apply h)
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example : ∀ (x : PUnit.{u}), x = PUnit.unit := by decide +kernel
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