feat: characterize BitVec.toInt in terms of BitVec.msb
#4200
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leodemoura
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semorrison
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Co-authored-by: Kim Morrison <[email protected]>
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I've addressed the comment, so this should be ready to merge now. |
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…r#4200) This PR extracts `msb_eq_false_iff_two_mul_lt` and `msb_eq_true_iff_two_mul_ge` from leanprover#4179, and uses them to prove a theorem that characterizes `BitVec.toInt` in terms of `BitVec.msb`. This lemma will be useful to prove a bit-blasting theorem for `BitVec.slt` and `BitVec.sle`. Also cleans up an existing proof (`toInt_eq_toNat_cond `), which turns out to be provable by `rfl`. --------- Co-authored-by: Kim Morrison <[email protected]>
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Prove theorems that relate `BitVec.slt` and `sle` to `carry`, so that these signed comparisons may be bitblasted in LeanSAT. This PR is stacked on top of #4200. For the diff without changes from that PR, see: opencompl/lean4@opencompl:lean4:bitvec-toInt-iff-msb...bitvec-slt-blast --------- Co-authored-by: Kim Morrison <[email protected]>
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This PR extracts
msb_eq_false_iff_two_mul_ltandmsb_eq_true_iff_two_mul_gefrom #4179, and uses them to prove a theorem that characterizesBitVec.toIntin terms ofBitVec.msb. This lemma will be useful to prove a bit-blasting theorem forBitVec.sltandBitVec.sle.Also cleans up an existing proof (
toInt_eq_toNat_cond), which turns out to be provable byrfl.