max/lean4-htt
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions 2

feat: add lemmas about BitVec.concat and bitwise ops (#3487)

Browse source 
Show how the various bitwise ops (`and`, `or`, `not`, and `xor`)
distribute over `concat`.
This commit is contained in:
Alex Keizer 2024-03-05 02:48:10 +00:00 • committed by GitHub
parent 89ec60befe
commit 46bf4b69b6
No known key found for this signature in database
GPG key ID: B5690EEEBB952194
1 changed files with 15 additions and 0 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

15
src/Init/Data/BitVec/Lemmas.lean
View file

@ -638,6 +638,21 @@ theorem getLsb_concat (x : BitVec w) (b : Bool) (i : Nat) :
@[simp] theorem getLsb_concat_succ : (concat x b).getLsb (i + 1) = x.getLsb i := by
simp [getLsb_concat]
@[simp] theorem not_concat (x : BitVec w) (b : Bool) : ~~~(concat x b) = concat (~~~x) !b := by
ext i; cases i using Fin.succRecOn <;> simp [*, Nat.succ_lt_succ]
@[simp] theorem concat_or_concat (x y : BitVec w) (a b : Bool) :
(concat x a) ||| (concat y b) = concat (x ||| y) (a || b) := by
ext i; cases i using Fin.succRecOn <;> simp
@[simp] theorem concat_and_concat (x y : BitVec w) (a b : Bool) :
(concat x a) &&& (concat y b) = concat (x &&& y) (a && b) := by
ext i; cases i using Fin.succRecOn <;> simp
@[simp] theorem concat_xor_concat (x y : BitVec w) (a b : Bool) :
(concat x a) ^^^ (concat y b) = concat (x ^^^ y) (xor a b) := by
ext i; cases i using Fin.succRecOn <;> simp
/-! ### add -/
theorem add_def {n} (x y : BitVec n) : x + y = .ofNat n (x.toNat + y.toNat) := rfl