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Proof step 23 from proof intshiftrsign-rec-neg (previous step)

0 ≤ j, i < 0, j < 32, 0 < j ⊦ i = ~1, bits2int(sublist(0, # int2bits((i - 1) / 2) + 1, mklist(true, i→n(j)) + int2bits((i - 1) / 2) + (i % 2 ≠ 0)')) = bits2int(sublist(0, # int2bits((i - 1) / 2), mklist(true, i→n(j - 1)) + int2bits((i - 1) / 2)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ m ≠ 0 → mklist(boolvar, m) = boolvar + mklist(boolvar, m - 1)
Proof step 25:
i→n(j) ≠ 0, 0 ≤ j, i < 0, j < 32, 0 < j ⊦ i = ~1, bits2int(sublist(0, # int2bits((i - 1) / 2) + 1, (true + mklist(true, i→n(j) - 1)) + int2bits((i - 1) / 2) + (i % 2 ≠ 0)')) = bits2int(sublist(0, # int2bits((i - 1) / 2), mklist(true, i→n(j - 1)) + int2bits((i - 1) / 2)))

Rule argument

seq: ⊦ m ≠ 0 → mklist(boolvar, m) = boolvar + mklist(boolvar, m - 1) subst: [m, boolvar] → [i→n(j), true] rotate: F spec: list-last inst: bitlista name: mk-rec

Additional information

Used simplifier rules: ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ mklist(boolvar, 0) = [];% ⊦ [] + bits = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;%n ≠ 0 ⊦ mklist(true, (* n)) = true ' + mklist(true, n -1);% ⊦ bits + [] = bits; Used terms: i→n(j), true