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Proof step 202 from proof int2bytes-rec-pos-any (previous step)

# int2bits(j % 2 ^ (i * 8)) = n * 8, bits2int(bytes2bits(bits2bytes(int2bits(j % 2 ^ (i * 8))))) < 0, n < i→n(i), 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), 0 < i ⊦ bits2bytes(mklist(false, 8 * i→n(i) - n * 8) + int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest, mklist(false, 8 * i→n(i) - n * 8) + int2bits(j % 2 ^ (i * 8)) = [], 1 + 8 * i→n(i) = n * 8, n = i→n(i), i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 203:
⊦ bits ≠ [] → (bits2int(bits) < 0 ↔ bits.first)
Proof step 204:
bytes2bits(bits2bytes(int2bits(j % 2 ^ (i * 8)))) ≠ [], # int2bits(j % 2 ^ (i * 8)) = n * 8, bytes2bits(bits2bytes(int2bits(j % 2 ^ (i * 8)))).first, n < i→n(i), 2 ^ (i * 8) ≤ j, 0 ≤ j % 2 ^ (i * 8), 0 < i ⊦ bits2bytes(mklist(false, 8 * i→n(i) - n * 8) + int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest, mklist(false, 8 * i→n(i) - n * 8) + int2bits(j % 2 ^ (i * 8)) = [], 1 + 8 * i→n(i) = n * 8, n = i→n(i), i = 0

Rule argument

seq: ⊦ bits ≠ [] → (bits2int(bits) < 0 ↔ bits.first) subst: [bits] → [bytes2bits(bits2bytes(int2bits(j % 2 ^ (i * 8))))] rotate: F spec: int2bits inst: name: bits2int-lez

Additional information

Used simplifier rules: bytes2bits-empty-01: ⊦ bytes2bits(bytes) = [] ↔ bytes = [];%bits2bytes-empty: ⊦ bits2bytes(bits) ≠ []; Used terms: bytes2bits(bits2bytes(int2bits(j % 2 ^ (i * 8))))