simproc Nat.reduceAnd doesn't work properly

[Rob23oba]

Prerequisites

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Description

The builtin simproc Nat.reduceAnd doesn't work. This is because of a typo in the definition:

builtin_dsimproc [simp, seval] reduceAnd ((_ &&& _ : Nat)) := reduceBin ``HOr.hOr 6 (· &&& ·)
-- should be
builtin_dsimproc [simp, seval] reduceAnd ((_ &&& _ : Nat)) := reduceBin ``HAnd.hAnd 6 (· &&& ·)

While there is a test for bitwise and reduction, it actually unintentionally uses lemmas other than Nat.reduceAnd:

#check_simp (3 : Nat) &&& (1 : Nat) ~> 1 -- uses Nat.and_one_is_mod, Nat.reduceMod

Example

/--
error: simp made no progress
-/
#guard_msgs in
example : 42 &&& 69 = 0 := by
  simp

Versions

This bug was introduced in v4.13.0-rc2 (the same version bitwise and reduction was introduced in).

Impact

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[nomeata]

Sounds plausible, thanks for the analysis. Do you want to prepare a PR? Including a regression test?

[Rob23oba]

Yeah, on it.