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Proof step 7 from proof int2int-lastn-negneg (previous step)

int2bits(i) = lastn(# int2bits(i), int2bits(i)), i < 0 ⊦ i + 2 ^ n→i(# int2bits(i)) = 0, i = i % 2 ^ n→i(# int2bits(i))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ abs(i) < j → i % j = i
Proof step 9:
¬ abs(i) < 2 ^ n→i(# int2bits(i)), int2bits(i) = lastn(# int2bits(i), int2bits(i)), i < 0 ⊦ i + 2 ^ n→i(# int2bits(i)) = 0, i = i % 2 ^ n→i(# int2bits(i))

Rule argument

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

Additional information

Used terms: 2 ^ n→i(# int2bits(i)), i