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Proof step 18 from proof cast-law-absorption (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ bits ≠ [] ∧ m ≤ n → lastn(m, fillsgn(n, bits)) = lastn(m, fillsgn(m, bits))

Rule argument

seq: ⊦ bits ≠ [] ∧ m ≤ n → lastn(m, fillsgn(n, bits)) = lastn(m, fillsgn(m, bits)) subst: [bits, n, m] → [int2bits(j), i→n(i0), i→n(i)] rotate: F spec: bitopsaux inst: name: fill-lastn-03

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ [];% ⊦ i→n(i) ≤ i→n(j) ↔ abs(i) ≤ abs(j);% ⊦ 0 < j → abs(j) = j;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: int2bits(j), i→n(i0), i→n(i)