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Proof step 25 from proof cast-help-comm (previous step)

# int2bits(j) < i→n(i), i ≤ i0, 1 < i0, 0 < i0, 0 < i, i < i0 ⊦ i0 = 0, bits2int(lastn(i→n(i), fillsgn(i→n(i0), int2bits(j)))) = bits2int(lastn(i→n(i0), fillsgn(i→n(i0), lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))))), i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits
Proof step 27:
# int2bits(j) ≤ i→n(i) ∧ int2bits(j) ≠ [], # int2bits(j) < i→n(i), i ≤ i0, 1 < i0, 0 < i0, 0 < i, i < i0 ⊦ i0 = 0, bits2int(lastn(i→n(i), fillsgn(i→n(i0), int2bits(j)))) = bits2int(lastn(i→n(i0), fillsgn(i→n(i0), lastn(i→n(i), mklist(int2bits(j).first, i→n(i) - # int2bits(j)) + int2bits(j))))), i = 0

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 simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m;% ⊦ int2bits(j) ≠ []; Used terms: int2bits(j), i→n(i)