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Proof step 28 from proof int2int-lastn-negneg (previous step)

i = (bits2int(bits) + 1) * 2 ^ n→i(m) + bits2int(lastn(m, int2bits(i))), int2bits(i) = bits + lastn(m, int2bits(i)), # bits = # int2bits(i) - m, bits2int(lastn(m, int2bits(i))) + 1 < 2 ^ n→i(m), i < 2 ^ n→i(m), i + 1 < 2 ^ n→i(m), 0 < 2 ^ n→i(m), bits2int(lastn(m, int2bits(i))) < 0, i < 0, m ≤ # int2bits(i), bits.first, bits2int(lastn(m, int2bits(i))) < 2 ^ n→i(m) ⊦ bits = [], m = 0, bits2int(lastn(m, int2bits(i))) = bits2int(lastn(m, int2bits(i))) % 2 ^ n→i(m), i + 2 ^ n→i(m) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ abs(i) < j → i % j = i
Proof step 30:
¬ abs(bits2int(lastn(m, int2bits(i)))) < 2 ^ n→i(m), i = (bits2int(bits) + 1) * 2 ^ n→i(m) + bits2int(lastn(m, int2bits(i))), int2bits(i) = bits + lastn(m, int2bits(i)), # bits = # int2bits(i) - m, bits2int(lastn(m, int2bits(i))) + 1 < 2 ^ n→i(m), i < 2 ^ n→i(m), i + 1 < 2 ^ n→i(m), 0 < 2 ^ n→i(m), bits2int(lastn(m, int2bits(i))) < 0, i < 0, m ≤ # int2bits(i), bits.first, bits2int(lastn(m, int2bits(i))) < 2 ^ n→i(m) ⊦ bits = [], m = 0, bits2int(lastn(m, int2bits(i))) = bits2int(lastn(m, int2bits(i))) % 2 ^ n→i(m), i + 2 ^ n→i(m) = 0

Rule argument

seq: ⊦ abs(i) < j → i % j = i subst: [j, i] → [2 ^ n→i(m), bits2int(lastn(m, int2bits(i)))] rotate: F spec: int-div inst: name: mod-zero-05

Additional information

Used terms: 2 ^ n→i(m), bits2int(lastn(m, int2bits(i)))