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

127 < i, 0 < i % 256, 127 < i % 256, 127 < i, 0 < i, 0 ≤ i ⊦ i % 256 = b2i(i2b(bits2int(lastn(8, int2bits(i))))) + 256

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 0 < i ∧ lastn(m, int2bits(i)).first ∧ m ≤ # int2bits(i) ∧ m ≠ 0 → bits2int(lastn(m, int2bits(i))) = i % 2 ^ n→i(m) - 2 ^ n→i(m)
Proof step 9:
¬(0 < i ∧ lastn(8, int2bits(i)).first ∧ 8 ≤ # int2bits(i) ∧ 8 ≠ 0), 127 < i, 0 < i % 256, 127 < i % 256, 127 < i, 0 < i, 0 ≤ i ⊦ i % 256 = b2i(i2b(bits2int(lastn(8, int2bits(i))))) + 256
Proof step 56:
0 < i ∧ lastn(8, int2bits(i)).first ∧ 8 ≤ # int2bits(i) ∧ 8 ≠ 0, 127 < i, 0 < i % 256, 127 < i % 256, 127 < i, 0 < i, 0 ≤ i ⊦ i % 256 = b2i(i2b(i % 2 ^ n→i(8) - 2 ^ n→i(8))) + 256

Rule argument

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

Additional information

Used terms: i, 8