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Proof step 13 from proof cast-help-comm (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ n ≤ # bits → fillsgn(n, bits) = bits subst: [bits, n] → [lastn(i→n(i0), fillsgn(i→n(i0), int2bits(j))), i→n(i)] rotate: F spec: bitopsaux inst: name: fillsgn-longer

Additional information

Used simplifier rules: ⊦ # lastn(n, bits) = n;% ⊦ i→n(i) ≤ i→n(j) ↔ abs(i) ≤ abs(j);% ⊦ 0 < j → abs(j) = j;% ⊦ 1 < i → abs(i) = i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i; Used terms: lastn(i→n(i0), fillsgn(i→n(i0), int2bits(j))), i→n(i)