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Proof step 84 from proof shiftright-rec-pos (previous step)

0 ≤ i, 0 ≤ i0, 1 < i, 0 < i, (mklist(false, i→n(i0)) + int2bits(i / 2)).first ⊦ bits2uint(firstn(# int2bits(i / 2), mklist(false, i→n(i0)) + int2bits(i / 2))) = bits2int(firstn(# int2bits(i / 2), mklist(false, i→n(i0)) + int2bits(i / 2))), mklist(false, i→n(i0)) + int2bits(i / 2) = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ n ≠ 0 → ((mklist(boolvar, n) + bits).first ↔ boolvar) subst: [bits, n, boolvar] → [int2bits(i / 2), i→n(i0), false] rotate: F spec: list-last inst: bitlista name: mk-first

Additional information

Used simplifier rules: ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ mklist(boolvar, 0) = [];% ⊦ [] + bits = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ int2bits(j) ≠ [];% ⊦ firstn(# bits, bits) = bits;% ⊦ bits2int(int2bits(i)) = i;% ⊦ int2bits(j).first ↔ j < 0;%0 < j ⊦ i / (* j) < 0 ↔ i + j ≤ 0;% ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j;% ⊦ i < 0 ∧ 0 < j → ¬ j ≤ i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: int2bits(i / 2), i→n(i0), false