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Proof step 4 from proof cast-mod-ls-neg (previous step)

0 < i, j < 0, 0 < 2 ^ (i - 1) + j ⊦ bits2int(lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))) = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits
Proof step 6:
¬(# int2bits(j) ≤ i→n(i) ∧ int2bits(j) ≠ []), 0 < i, j < 0, 0 < 2 ^ (i - 1) + j ⊦ bits2int(lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))) = j
Proof step 12:
# int2bits(j) ≤ i→n(i) ∧ int2bits(j) ≠ [], 0 < i, j < 0, 0 < 2 ^ (i - 1) + j ⊦ bits2int(lastn(i→n(i), mklist(int2bits(j).first, i→n(i) - # int2bits(j)) + int2bits(j))) = j

Rule argument

seq: ⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits subst: [bits, n] → [int2bits(j), i→n(i)] rotate: F spec: bitopsaux inst: name: fill-fill

Additional information

Used terms: int2bits(j), i→n(i)