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.
86 lines
2.6 KiB
Text
86 lines
2.6 KiB
Text
import Lean
|
|
|
|
inductive Tree
|
|
| leaf : Tree
|
|
| node : Tree → Tree → Tree
|
|
|
|
abbrev notSubtree (x : Tree) (t : Tree) : Prop :=
|
|
t.rec True fun l r l_ih r_ih => (x ≠ l ∧ l_ih) ∧ (x ≠ r ∧ r_ih)
|
|
|
|
infix:50 "≮" => notSubtree
|
|
|
|
theorem Tree.acyclic (x t : Tree) : x = t → x ≮ t := by
|
|
let rec right (x s : Tree) (b : Tree) (h : x ≮ b) : node s x ≠ b ∧ node s x ≮ b := by
|
|
match b, h with
|
|
| leaf, h =>
|
|
apply And.intro _ trivial
|
|
intro h; injection h
|
|
| node l r, h =>
|
|
have ihl : x ≮ l → node s x ≠ l ∧ node s x ≮ l := right x s l
|
|
have ihr : x ≮ r → node s x ≠ r ∧ node s x ≮ r := right x s r
|
|
have hl : x ≠ l ∧ x ≮ l := h.1
|
|
have hr : x ≠ r ∧ x ≮ r := h.2
|
|
have ihl : node s x ≠ l ∧ node s x ≮ l := ihl hl.2
|
|
have ihr : node s x ≠ r ∧ node s x ≮ r := ihr hr.2
|
|
apply And.intro
|
|
focus
|
|
intro h
|
|
injection h with _ h
|
|
exact absurd h hr.1
|
|
done
|
|
focus
|
|
apply And.intro
|
|
apply ihl
|
|
apply ihr
|
|
let rec left (x t : Tree) (b : Tree) (h : x ≮ b) : node x t ≠ b ∧ node x t ≮ b := by
|
|
match b, h with
|
|
| leaf, h =>
|
|
apply And.intro _ trivial
|
|
intro h; injection h
|
|
| node l r, h =>
|
|
have ihl : x ≮ l → node x t ≠ l ∧ node x t ≮ l := left x t l
|
|
have ihr : x ≮ r → node x t ≠ r ∧ node x t ≮ r := left x t r
|
|
have hl : x ≠ l ∧ x ≮ l := h.1
|
|
have hr : x ≠ r ∧ x ≮ r := h.2
|
|
have ihl : node x t ≠ l ∧ node x t ≮ l := ihl hl.2
|
|
have ihr : node x t ≠ r ∧ node x t ≮ r := ihr hr.2
|
|
apply And.intro
|
|
focus
|
|
intro h
|
|
injection h with h _
|
|
exact absurd h hl.1
|
|
done
|
|
focus
|
|
apply And.intro
|
|
apply ihl
|
|
apply ihr
|
|
let rec aux : (x : Tree) → x ≮ x
|
|
| leaf => trivial
|
|
| node l r => by
|
|
have ih₁ : l ≮ l := aux l
|
|
have ih₂ : r ≮ r := aux r
|
|
show (node l r ≠ l ∧ node l r ≮ l) ∧ (node l r ≠ r ∧ node l r ≮ r)
|
|
apply And.intro
|
|
focus
|
|
apply left
|
|
assumption
|
|
focus
|
|
apply right
|
|
assumption
|
|
intro h
|
|
subst h
|
|
apply aux
|
|
|
|
open Tree
|
|
|
|
theorem ex1 (x : Tree) : x ≠ node leaf (node x leaf) := by
|
|
intro h
|
|
exact absurd rfl $ Tree.acyclic _ _ h |>.2.2.1.1
|
|
|
|
theorem ex2 (x : Tree) : x ≠ node x leaf := by
|
|
intro h
|
|
exact absurd rfl $ Tree.acyclic _ _ h |>.1.1
|
|
|
|
theorem ex3 (x y : Tree) : x ≠ node y x := by
|
|
intro h
|
|
exact absurd rfl $ Tree.acyclic _ _ h |>.2.1
|