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feat: BitVec.getMsbD_[ofNatLt|allOnes|not] #6149

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Nov 21, 2024
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feat: BitVec.getMsbD_[ofNatLt|allOnes|not] #6149

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12 changes: 12 additions & 0 deletions src/Init/Data/BitVec/Lemmas.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -269,6 +269,10 @@ theorem ofBool_eq_iff_eq : ∀ {b b' : Bool}, BitVec.ofBool b = BitVec.ofBool b'
getLsbD (x#'lt) i = x.testBit i := by
simp [getLsbD, BitVec.ofNatLt]

@[simp] theorem getMsbD_ofNatLt {n x i : Nat} (h : x < 2^n) :
getMsbD (x#'h) i = (decide (i < n) && x.testBit (n - 1 - i)) := by
simp [getMsbD, getLsbD]

@[simp, bv_toNat] theorem toNat_ofNat (x w : Nat) : (BitVec.ofNat w x).toNat = x % 2^w := by
simp [BitVec.toNat, BitVec.ofNat, Fin.ofNat']

Expand Down Expand Up @@ -755,6 +759,10 @@ theorem extractLsb'_eq_extractLsb {w : Nat} (x : BitVec w) (start len : Nat) (h
@[simp] theorem getLsbD_allOnes : (allOnes v).getLsbD i = decide (i < v) := by
simp [allOnes]

@[simp] theorem getMsbD_allOnes : (allOnes v).getMsbD i = decide (i < v) := by
simp [allOnes]
omega

@[simp] theorem getElem_allOnes (i : Nat) (h : i < v) : (allOnes v)[i] = true := by
simp [getElem_eq_testBit_toNat, h]

Expand Down Expand Up @@ -1007,6 +1015,10 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
@[simp] theorem getLsbD_not {x : BitVec v} : (~~~x).getLsbD i = (decide (i < v) && ! x.getLsbD i) := by
by_cases h' : i < v <;> simp_all [not_def]

@[simp] theorem getMsbD_not {x : BitVec v} :
(~~~x).getMsbD i = (decide (i < v) && ! x.getMsbD i) := by
by_cases h' : i < v <;> simp_all [not_def]

@[simp] theorem getElem_not {x : BitVec w} {i : Nat} (h : i < w) : (~~~x)[i] = !x[i] := by
simp only [getElem_eq_testBit_toNat, toNat_not]
rw [← Nat.sub_add_eq, Nat.add_comm 1]
Expand Down
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