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Proof step 83 from proof cast-help-comm (previous step)

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

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] → [int2bits(j), i→n(i0)] rotate: F spec: bitopsaux inst: name: fill-fill

Additional information

Used simplifier rules: ⊦ int2bits(j).first ↔ j < 0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ n ≤ # bits → lastn(n, bits0 + bits) = lastn(n, bits);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ int2bits(j) ≠ []; Used terms: int2bits(j), i→n(i0)