feat: lemmas for Bitvector division when denominator is zero #5609
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These lemmas explain what happens when the denominator is zero. This is used by bv_decide for bitblasting.
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| theorem sdiv_zero_eq (x : BitVec n) : x.sdiv 0#n = 0#n := by | ||
| simp only [sdiv_eq, msb_zero] |
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| theorem sdiv_zero_eq (x : BitVec n) : x.sdiv 0#n = 0#n := by | |
| simp only [sdiv_eq, msb_zero] | |
| @[simp] | |
| theorem sdiv_zero {x : BitVec n} : x.sdiv 0#n = 0#n := by | |
| simp only [sdiv_eq, msb_zero] |
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| theorem smod_zero_eq (x : BitVec n) : x.smod 0#n = x := by |
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| theorem smod_zero_eq (x : BitVec n) : x.smod 0#n = x := by | |
| @[simp] | |
| theorem smod_zero {x : BitVec n} : x.smod 0#n = x := by |
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I think you can also drop the |
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These lemmas explain what happens when the denominator is zero with
udiv,umod,sdiv,smod. A follow-up PR will show what happens withsmtUDivandsmtSMod, since these need some more bitvector theory.These lemmas will be used by
bv_decidefor bitblasting.The theorems
{sdiv, smod}_zero_eqare located afternegtheory has been built for the purpose of writing terse proofs.