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Proof step 71 from proof cast-help-comm (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: ⊦ n ≤ # bits → # 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;% ⊦ lastn(n, bits) = [] ↔ n = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ lastn(0, bits) = [];% ⊦ fillsgn(n, []) = mklist(false, n);% ⊦ lastn(n, mklist(boolvar, n)) = mklist(boolvar, n);% ⊦ i ≠ j → (i ≤ j ↔ i < j); Used terms: lastn(i→n(i), int2bits(j)), i→n(i0)