lean4-htt/tests/elab/inj2.lean
Garmelon 08eb78a5b2
chore: switch to new test/bench suite (#12590)
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.
2026-02-25 13:51:53 +00:00

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universe u v
inductive Vec2 (α : Type u) (β : Type v) : Nat → Type (max u v)
| nil : Vec2 α β 0
| cons : α → β → forall {n}, Vec2 α β n → Vec2 α β (n+1)
inductive Fin2 : Nat → Type
| zero (n : Nat) : Fin2 (n+1)
| succ {n : Nat} (s : Fin2 n) : Fin2 (n+1)
theorem test1 {α β} {n} (a₁ a₂ : α) (b₁ b₂ : β) (v w : Vec2 α β n) (h : Vec2.cons a₁ b₁ v = Vec2.cons a₂ b₂ w) : a₁ = a₂ :=
by {
injection h
}
theorem test2 {α β} {n} (a₁ a₂ : α) (b₁ b₂ : β) (v w : Vec2 α β n) (h : Vec2.cons a₁ b₁ v = Vec2.cons a₂ b₂ w) : v = w :=
by {
injection h with h1 h2 h3 h4
}
theorem test3 {α β} {n} (a₁ a₂ : α) (b₁ b₂ : β) (v w : Vec2 α β n) (f : Vec2 α β n → Nat) (h : Vec2.cons a₁ b₁ v = Vec2.cons a₂ b₂ w) : f v = f w :=
by {
injection h with _ _ _ h4;
rw [h4]
}
def test4 {α} (v : Fin2 0) : α :=
by cases v
def test5 {α β} {n} (v : Vec2 α β (n+1)) : α := by
cases v with
| cons h1 h2 tail => exact h1
def test6 {α β} {n} (v : Vec2 α β (n+2)) : α := by
cases v with
| cons h1 h2 tail => exact h1