ad3b0b4a2c
This commit also fixes a bug when using multiple targets with the `induction` and `cases` tactics.
47 lines
1.6 KiB
Text
47 lines
1.6 KiB
Text
def Vec (α : Type u) (n : Nat) : Type u := { a : List α // a.length = n }
|
||
def Vec.nil : Vec α 0 := ⟨[], rfl⟩
|
||
def Vec.cons (a : α) (as : Vec α n) : Vec α (n+1) := ⟨a :: as.val, by simp [as.property]⟩
|
||
|
||
set_option pp.analyze false
|
||
|
||
def Vec.casesOn
|
||
(motive : (n : Nat) → Vec α n → Sort v)
|
||
(n : Nat)
|
||
(as : Vec α n)
|
||
(nil : motive 0 Vec.nil)
|
||
(cons : (n : Nat) → (a : α) → (as : Vec α n) → (ih : motive n as) → motive (n+1) (Vec.cons a as))
|
||
: motive n as :=
|
||
let rec go (n : Nat) (as : List α) (h : as.length = n) : motive n ⟨as, h⟩ :=
|
||
match n, as, h with
|
||
| 0, [], _ => nil
|
||
| n+1, a::as, h =>
|
||
have : as.length = n := by injection h; assumption
|
||
have ih : motive n ⟨as, this⟩ := go n as this
|
||
cons n a ⟨as, this⟩ ih
|
||
match as with
|
||
| ⟨as, h⟩ => go n as h
|
||
|
||
example (n : Nat) (a : α) (as : Vec α n) : Vec.cons a (Vec.cons a as) = Vec.cons a (Vec.cons a as) := by
|
||
induction n+2, Vec.cons a (Vec.cons a as) using Vec.casesOn
|
||
case nil => constructor
|
||
case cons n a as ih =>
|
||
traceState
|
||
constructor
|
||
|
||
#print "-----"
|
||
|
||
example (n : Nat) (a : α) (as : Vec α n) : Vec.cons a (Vec.cons a as) = Vec.cons a (Vec.cons a as) := by
|
||
cases n+2, Vec.cons a (Vec.cons a as) using Vec.casesOn
|
||
case nil => constructor
|
||
case cons n a as ih =>
|
||
traceState
|
||
constructor
|
||
|
||
#print "-----"
|
||
|
||
example (n : Nat) (a : α) (as : Vec α n) : Vec.cons a (Vec.cons a as) = Vec.cons a (Vec.cons a as) := by
|
||
cases h₁ : n+2, h₂ : Vec.cons a (Vec.cons a as) using Vec.casesOn
|
||
case nil => constructor
|
||
case cons n' a' as' ih =>
|
||
traceState
|
||
constructor
|