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chore: two BitVec lemmas that help simp confluence (#6807)

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This PR adds two simple `BitVec` lemmas which improve `simp` local
confluence.
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Kim Morrison 2025-01-28 12:12:05 +11:00 • committed by GitHub
parent 4d66e7bdc0
commit eb1c9b9ab2
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1 changed files with 15 additions and 1 deletions
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16
src/Init/Data/BitVec/Lemmas.lean
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@ -378,6 +378,16 @@ theorem getElem_ofBool {b : Bool} : (ofBool b)[0] = b := by simp
@[simp] theorem msb_ofBool (b : Bool) : (ofBool b).msb = b := by
cases b <;> simp [BitVec.msb]
@[simp] theorem one_eq_zero_iff : 1#w = 0#w ↔ w = 0 := by
constructor
· intro h
cases w
· rfl
· replace h := congrArg BitVec.toNat h
simp at h
· rintro rfl
simp
/-! ### msb -/
@[simp] theorem msb_zero : (0#w).msb = false := by simp [BitVec.msb, getMsbD]
@ -1164,6 +1174,10 @@ theorem not_not {b : BitVec w} : ~~~(~~~b) = b := by
ext i h
simp [h]
@[simp] theorem and_not_self (x : BitVec n) : x &&& ~~~x = 0 := by
ext i
simp_all
theorem not_eq_comm {x y : BitVec w} : ~~~ x = y ↔ x = ~~~ y := by
constructor
· intro h
@ -3429,7 +3443,7 @@ theorem shiftLeft_eq_mul_twoPow (x : BitVec w) (n : Nat) :
simp [getLsbD_shiftLeft, Fin.is_lt, decide_true, Bool.true_and, mul_twoPow_eq_shiftLeft]
/-- 2^i * 2^j = 2^(i + j) with bitvectors as well -/
theorem twoPow_mul_twoPow_eq {w : Nat} (i j : Nat) : twoPow w i * twoPow w j = twoPow w (i + j) := by
theorem twoPow_mul_twoPow_eq {w : Nat} (i j : Nat) : twoPow w i * twoPow w j = twoPow w (i + j) := by
apply BitVec.eq_of_toNat_eq
simp only [toNat_mul, toNat_twoPow]
rw [← Nat.mul_mod, Nat.pow_add]