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Proof step 58 from proof bytes2int-append (previous step)

bytes2bits(bytes).first, 0 ≤ bits2int(bytes2bits(bytes0)) ⊦ bytes = [], bytes0 = [], bytes2bits(bytes) + bytes2bits(bytes0) = [], bitsinvert(bytes2bits(bytes)) + bitsinvert(bytes2bits(bytes0)) = [], bits2int(bytes2bits(bytes0)) % 2 ^ (8 * n→i(# bytes0)) = bits2int(bytes2bits(bytes0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 59:
⊦ abs(i) < j → i % j = i
Proof step 60:
¬ abs(bits2int(bytes2bits(bytes0))) < 2 ^ (8 * n→i(# bytes0)), bytes2bits(bytes).first, 0 ≤ bits2int(bytes2bits(bytes0)) ⊦ bytes = [], bytes0 = [], bytes2bits(bytes) + bytes2bits(bytes0) = [], bitsinvert(bytes2bits(bytes)) + bitsinvert(bytes2bits(bytes0)) = [], bits2int(bytes2bits(bytes0)) % 2 ^ (8 * n→i(# bytes0)) = bits2int(bytes2bits(bytes0))

Rule argument

seq: ⊦ abs(i) < j → i % j = i subst: [j, i] → [2 ^ (8 * n→i(# bytes0)), bits2int(bytes2bits(bytes0))] rotate: F spec: int-div inst: name: mod-zero-05

Additional information

Used terms: 2 ^ (8 * n→i(# bytes0)), bits2int(bytes2bits(bytes0))