feat: add BitVec.neg_neg #14
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tobiasgrosser
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AtticusKuhn
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src/Init/Data/BitVec/Lemmas.lean
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| @[simp] | ||
| theorem neg_neg {x : BitVec w} : - - x = x := by | ||
| by_cases h : x = 0 | ||
| · subst h | ||
| simp | ||
| · simp only [toNat_eq, toNat_neg] | ||
| rw [toNat_eq] at h | ||
| simp only [ofNat_eq_ofNat, toNat_ofNat, Nat.zero_mod] at h | ||
| rw [Nat.mod_eq_of_lt (a := 2 ^ w - x.toNat) (by omega)] | ||
| rw [Nat.mod_eq_of_lt (by omega)] | ||
| omega |
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Perhaps this theorem could be made simpler?
@[simp]
theorem neg_neg2 {x : BitVec w} : - - x = x := by
have p : (- x) + (- -x) = x - x := by
simp [BitVec.sub_self, ← BitVec.sub_toAdd]
rw [BitVec.eq_sub_iff_add_eq , BitVec.add_comm, ← BitVec.add_assoc , ← BitVec.sub_toAdd x x , BitVec.sub_self x, BitVec.zero_add] at p
assumption
tobiasgrosser
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.. as well as neg_neq_iff_neq_neg.
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Co-authored-by: Henrik Böving <hargonix@gmail.com>
|
Merged with leanprover#4951 into lean. |
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... as well as neg_neq_iff_neq_neg.