mirror of
https://github.com/leanprover/lean4.git
synced 2026-03-17 18:34:06 +00:00
08eb78a5b2
This PR sets up the new integrated test/bench suite. It then migrates all benchmarks and some related tests to the new suite. There's also some documentation and some linting. For now, a lot of the old tests are left alone so this PR doesn't become even larger than it already is. Eventually, all tests should be migrated to the new suite though so there isn't a confusing mix of two systems.
53 lines
1.6 KiB
Lean4
53 lines
1.6 KiB
Lean4
opaque double : Nat → Nat
|
||
def P (n : Nat) : Prop := n >= 0
|
||
theorem pax (n : Nat) : P n := by grind [P]
|
||
def T (n : Nat) : Type := Vector Nat n
|
||
|
||
inductive Foo' (α β : Type u) : (n : Nat) → P n -> Type u
|
||
| even (a : α) (n : Nat) (v : T n) (h : P n) : Foo' α β (double n) (pax _)
|
||
| odd (b : β) (n : Nat) (v : T n) : Foo' α β (Nat.succ (double n)) (pax _)
|
||
|
||
example (α β : Type) (a₁ a₂ : α)
|
||
(n₁ n₂ : Nat)
|
||
(v₁ : T n₁) (v₂ : T n₂)
|
||
(h₁ : P n₁) (h₂ : P n₂)
|
||
(h_1 : double n₁ = double n₂)
|
||
(h_2 : Foo'.even (β := β) a₁ n₁ v₁ h₁ ≍ Foo'.even (β := β) a₂ n₂ v₂ h₂) :
|
||
a₁ = a₂ ∧ n₁ = n₂ ∧ v₁ ≍ v₂ ∧ h₁ ≍ h₂ := by
|
||
grind
|
||
|
||
example (α β : Type) (a : α) (b : β)
|
||
(n₁ n₂ : Nat)
|
||
(v₁ : T n₁) (v₂ : T n₂)
|
||
(h₁ : P n₁)
|
||
(h_1 : double n₁ = (double n₂).succ)
|
||
(h_2 : Foo'.even (β := β) a n₁ v₁ h₁ ≍ Foo'.odd (α := α) b n₂ v₂)
|
||
: False := by
|
||
grind
|
||
|
||
inductive Parity : Nat -> Type
|
||
| even (n) : Parity (double n)
|
||
| odd (n) : Parity (Nat.succ (double n))
|
||
|
||
example
|
||
(motive : (x : Nat) → Parity x → Sort u_1)
|
||
(h_2 : (j : Nat) → motive (double j) (Parity.even j))
|
||
(j n : Nat)
|
||
(heq_1 : double n = double j)
|
||
(heq_2 : Parity.even n ≍ Parity.even j):
|
||
h_2 n ≍ h_2 j := by
|
||
grind
|
||
|
||
opaque q : Nat → Nat → Prop
|
||
axiom qax : q a b → double a = double b
|
||
attribute [grind →] qax
|
||
|
||
example
|
||
(motive : (x : Nat) → Parity x → Sort u_1)
|
||
(h_2 : (j : Nat) → motive (double j) (Parity.even j))
|
||
(j n : Nat)
|
||
(heq_1 : q j n)
|
||
(heq_2 : Parity.even n ≍ Parity.even j):
|
||
h_2 n ≍ h_2 j := by
|
||
grind
|