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

feat: add BitVec.(msb, getMsbD)_concat (#5865)

Browse source
This commit is contained in:
Luisa Cicolini 2024-10-28 12:10:02 +00:00 • committed by GitHub
parent f558402ab8
commit 2f1dc878e4
No known key found for this signature in database
GPG key ID: B5690EEEBB952194
1 changed files with 25 additions and 0 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

25
src/Init/Data/BitVec/Lemmas.lean
View file

@ -1917,6 +1917,31 @@ theorem toNat_shiftConcat_lt_of_lt {x : BitVec w} {b : Bool} {k : Nat}
ext
simp [getLsbD_concat]
@[simp]
theorem getMsbD_concat {i w : Nat} {b : Bool} {x : BitVec w} :
(x.concat b).getMsbD i = if i < w then x.getMsbD i else decide (i = w) && b := by
simp only [getMsbD_eq_getLsbD, Nat.add_sub_cancel, getLsbD_concat]
by_cases h₀ : i = w
· simp [h₀]
· by_cases h₁ : i < w
· simp [h₀, h₁, show ¬ w - i = 0 by omega, show i < w + 1 by omega, Nat.sub_sub, Nat.add_comm]
· simp only [show w - i = 0 by omega, ↓reduceIte, h₁, h₀, decide_False, Bool.false_and,
Bool.and_eq_false_imp, decide_eq_true_eq]
intro
omega
@[simp]
theorem msb_concat {w : Nat} {b : Bool} {x : BitVec w} :
(x.concat b).msb = if 0 < w then x.msb else b := by
simp only [BitVec.msb, getMsbD_eq_getLsbD, Nat.zero_lt_succ, decide_True, Nat.add_one_sub_one,
Nat.sub_zero, Bool.true_and]
by_cases h₀ : 0 < w
· simp only [Nat.lt_add_one, getLsbD_eq_getElem, getElem_concat, h₀, ↓reduceIte, decide_True,
Bool.true_and, ite_eq_right_iff]
intro
omega
· simp [h₀, show w = 0 by omega]
/-! ### add -/
theorem add_def {n} (x y : BitVec n) : x + y = .ofNat n (x.toNat + y.toNat) := rfl