feat: add BitVec.getLsb_concat
#3457
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src/Init/Data/BitVec/Lemmas.lean
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| (concat x b).getLsb i = match i with | ||
| | 0 => b | ||
| | i+1 => x.getLsb i := by |
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I'm skeptical of this as a simp lemma with the match on the RHS.
The @[simp] lemmas should be for getLsb_concat_zero and getLsb_concat_succ.
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| theorem toNat_le_one (c:Bool) : c.toNat ≤ 1 := by | ||
| cases c <;> trivial | ||
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| theorem toNat_lt (b : Bool) : b.toNat < 2 := | ||
| Nat.lt_succ_of_le (toNat_le_one _) |
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I would prefer consistent names here, but I think toNat_lt is correct, so will rename the other one.
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To merge after #3457. --------- Co-authored-by: Alex Keizer <[email protected]>
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First (baby)-step to a
concat-basedbitblast: a characterization ofconcatin terms ofgetLsb.The proof might benefit slightly from a
toNat_concatlemma, but I wasn't sure what the normal form there should be, so I avoided it.