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Proof step 10 from proof bib-pos-high (previous step)

0 < i % 256, 127 < i % 256, 127 < i, 0 < i ⊦ i % 256 = b2i(i2b(bits2int(lastn(8, int2bits(i))))) + 256, 0 = i, lastn(8, int2bits(i)).first ∧ ¬ # int2bits(i) < 8

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 0 < i → (# int2bits(i) < m ↔ i < 2 ^ (n→i(m) - 2))
Proof step 12:
0 < i, 0 < i % 256, 127 < i % 256, 127 < i, 0 < i ⊦ i % 256 = b2i(i2b(bits2int(lastn(8, int2bits(i))))) + 256, 0 = i, lastn(8, int2bits(i)).first ∧ ¬ i < 2 ^ (n→i(8) - 2)

Rule argument

seq: ⊦ 0 < i → (# int2bits(i) < m ↔ i < 2 ^ (n→i(m) - 2)) subst: [m, i] → [8, i] rotate: F spec: int2bits inst: name: int2bits-lslen

Additional information

Used terms: 8, i