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feat: BitVec.toInt_shiftLeft theorem (#6346)

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This PR completes the toNat/Int/Fin family for `shiftLeft`.
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Harun Khan 2025-01-07 21:55:50 -05:00 • committed by GitHub
parent 18b183f62b
commit 91cbd7c80e
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1 changed files with 7 additions and 2 deletions
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src/Init/Data/BitVec/Lemmas.lean
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@ -1142,11 +1142,16 @@ theorem getMsb_not {x : BitVec w} :
/-! ### shiftLeft -/
@[simp, bv_toNat] theorem toNat_shiftLeft {x : BitVec v} :
BitVec.toNat (x <<< n) = BitVec.toNat x <<< n % 2^v :=
(x <<< n).toNat = x.toNat <<< n % 2^v :=
BitVec.toNat_ofNat _ _
@[simp] theorem toInt_shiftLeft {x : BitVec w} :
(x <<< n).toInt = (x.toNat <<< n : Int).bmod (2^w) := by
rw [toInt_eq_toNat_bmod, toNat_shiftLeft, Nat.shiftLeft_eq]
simp
@[simp] theorem toFin_shiftLeft {n : Nat} (x : BitVec w) :
BitVec.toFin (x <<< n) = Fin.ofNat' (2^w) (x.toNat <<< n) := rfl
(x <<< n).toFin = Fin.ofNat' (2^w) (x.toNat <<< n) := rfl
@[simp]
theorem shiftLeft_zero (x : BitVec w) : x <<< 0 = x := by