lean4-htt/tests/playground/simp_binders.lean
2021-03-09 15:09:51 -08:00

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Text

axiom let_in {A B} (x : A) (f : A -> B) : B
axiom add (x y : Nat) : Nat
@[simp] axiom addZero (x : Nat) : add x 0 = x
syntax "bigAdd0Seq! " num term:max : term
syntax "bigAddSeq! " num term:max : term
macro_rules
| `(bigAdd0Seq! $n $acc) =>
let n := n.toNat
if n == 0 then
`(add $acc (add $acc 0))
else
`(let_in (add $acc (add $acc 0)) (fun acc' => bigAdd0Seq! $(Lean.quote (n - 1)) acc'))
macro_rules
| `(bigAddSeq! $n $acc) =>
let n := n.toNat
if n == 0 then
`(add $acc $acc)
else
`(let_in (add $acc $acc) (fun acc' => bigAddSeq! $(Lean.quote (n - 1)) acc'))
theorem ex1 (x : Nat) : bigAdd0Seq! 150 x = bigAddSeq! 150 x := by
simp
-- theorem ex2 (x : Nat) : bigAddSeq! 5 x = bigAddSeq! 5 x := by
-- simp