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Proof step 7 from proof bib-neg-high (previous step)

i < ~128, i ≤ ~256, ~128 ≤ i % 256, i < 0 ⊦ b2i(i2b(bits2int(lastn(8, int2bits(i))))) = i % 256

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ i < 0 ∧ lastn(m, int2bits(i)).first ∧ m ≤ # int2bits(i) ∧ m ≠ 0 ∧ ~ i ≠ 2 ^ n→i(m) → bits2int(lastn(m, int2bits(i))) = i % 2 ^ n→i(m)
Proof step 9:
¬(i < 0 ∧ lastn(8, int2bits(i)).first ∧ 8 ≤ # int2bits(i) ∧ 8 ≠ 0 ∧ ~ i ≠ 2 ^ n→i(8)), i < ~128, i ≤ ~256, ~128 ≤ i % 256, i < 0 ⊦ b2i(i2b(bits2int(lastn(8, int2bits(i))))) = i % 256
Proof step 71:
i < 0 ∧ lastn(8, int2bits(i)).first ∧ 8 ≤ # int2bits(i) ∧ 8 ≠ 0 ∧ ~ i ≠ 2 ^ n→i(8), i < ~128, i ≤ ~256, ~128 ≤ i % 256, i < 0 ⊦ b2i(i2b(i % 2 ^ n→i(8))) = i % 256

Rule argument

spec: int2bits inst: name: int2int-lastn-negneg seq: ⊦ i < 0 ∧ lastn(m, int2bits(i)).first ∧ m ≤ # int2bits(i) ∧ m ≠ 0 ∧ ~ i ≠ 2 ^ n→i(m) → bits2int(lastn(m, int2bits(i))) = i % 2 ^ n→i(m) subst: [i, m] → [i, 8] flags: rewrite

Additional information

Used terms: i, 8