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Proof step 251 from proof int2bytes-rec-pos-any (previous step)

0 ≤ j, 0 < j, 256 ≤ j, # int2bits(j % 256) < 8, 0 ≤ b2i(i2b(j % 256)) ⊦ mklist(false, 8 - # int2bits(j % 256)) + int2bits(j % 256) = [], 9 = # int2bits(j % 256), # int2bits(j % 256) = 8, i2b(bits2int(mklist(false, 8 - # int2bits(j % 256)) + int2bits(j % 256))) = i2b(j % 256), bits2int(mklist(false, 8 - # int2bits(j % 256)) + int2bits(j % 256)) = j % 256

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 252:
⊦ n ≠ 0 → bits2int(mklist(false, n) + bits) = bits2int(false ' + bits)
Proof step 253:
8 - # int2bits(j % 256) ≠ 0, 0 ≤ j, 0 < j, 256 ≤ j, # int2bits(j % 256) < 8, 0 ≤ b2i(i2b(j % 256)) ⊦ mklist(false, 8 - # int2bits(j % 256)) + int2bits(j % 256) = [], 9 = # int2bits(j % 256), # int2bits(j % 256) = 8, i2b(bits2int(false ' + int2bits(j % 256))) = i2b(j % 256), bits2int(false ' + int2bits(j % 256)) = j % 256

Rule argument

seq: ⊦ n ≠ 0 → bits2int(mklist(false, n) + bits) = bits2int(false ' + bits) subst: [bits, n] → [int2bits(j % 256), 8 - # int2bits(j % 256)] rotate: F spec: int2bits inst: name: bits2int-zeros

Additional information

Used simplifier rules: ⊦ n < m → m - n ≠ 0; Used terms: int2bits(j % 256), 8 - # int2bits(j % 256)