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feat: add BitVec.[not_not, allOnes_shiftLeft_or_shiftLeft, allOnes_shiftLeft_and_shiftLeft] #5469

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merged 7 commits into from
Sep 25, 2024
Merged

feat: add BitVec.[not_not, allOnes_shiftLeft_or_shiftLeft, allOnes_shiftLeft_and_shiftLeft] #5469

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4c57f99
added some shiftLeft and not theorems
luisacicolini Sep 25, 2024
82aeae1
Update src/Init/Data/BitVec/Lemmas.lean
luisacicolini Sep 25, 2024
8a8f68a
Update src/Init/Data/BitVec/Lemmas.lean
luisacicolini Sep 25, 2024
0f97b43
dropped misplaced thm
luisacicolini Sep 25, 2024
62e2ee4
Merge branch 'shift-theorems' of github.com:opencompl/lean4 into shif…
luisacicolini Sep 25, 2024
0b996a9
addressed comment
luisacicolini Sep 25, 2024
17f27e2
fixed bv_normalize
luisacicolini Sep 25, 2024
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15 changes: 15 additions & 0 deletions src/Init/Data/BitVec/Lemmas.lean
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Expand Up @@ -939,6 +939,11 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
ext i
simp

@[simp]
theorem not_not {b : BitVec w} : ~~~(~~~b) = b := by
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ext i
simp

/-! ### cast -/

@[simp] theorem not_cast {x : BitVec w} (h : w = w') : ~~~(cast h x) = cast h (~~~x) := by
Expand Down Expand Up @@ -1072,6 +1077,16 @@ theorem shiftLeft_add {w : Nat} (x : BitVec w) (n m : Nat) :
cases h₅ : decide (i < n + m) <;>
simp at * <;> omega

@[simp]
theorem allOnes_shiftLeft_and_shiftLeft {x : BitVec w} {n : Nat} :
BitVec.allOnes w <<< n &&& x <<< n = x <<< n := by
simp [← BitVec.shiftLeft_and_distrib]

@[simp]
theorem allOnes_shiftLeft_or_shiftLeft {x : BitVec w} {n : Nat} :
BitVec.allOnes w <<< n ||| x <<< n = BitVec.allOnes w <<< n := by
simp [← shiftLeft_or_distrib]

@[deprecated shiftLeft_add (since := "2024-06-02")]
theorem shiftLeft_shiftLeft {w : Nat} (x : BitVec w) (n m : Nat) :
(x <<< n) <<< m = x <<< (n + m) := by
Expand Down
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