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Proof step 29 from proof shiftzero-rec-neg-shorter (previous step)

i→n(j) = m0 + 1, # int2bits((i - 1) / 2) ≤ m, i < ~1, i < 0, 1 < j, 0 < j ⊦ i = ~1, j = 0, bits2uint(firstn(m, mklist(false, m0) + fillsgn(m + 1, int2bits((i - 1) / 2) + (i % 2 ≠ 0)'))) = bits2int(firstn(m, mklist(false, m0) + fillsgn(m, int2bits((i - 1) / 2))))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ n ≠ 0 ∧ bits ≠ [] → fillsgn(n, bits + boolvar ') = fillsgn(n -1, bits) + boolvar
Proof step 31:
m + 1 ≠ 0 ∧ int2bits((i - 1) / 2) ≠ [], i→n(j) = m0 + 1, # int2bits((i - 1) / 2) ≤ m, i < ~1, i < 0, 1 < j, 0 < j ⊦ i = ~1, j = 0, bits2uint(firstn(m, mklist(false, m0) + (fillsgn((m + 1)-1, int2bits((i - 1) / 2)) + (i % 2 ≠ 0)))) = bits2int(firstn(m, mklist(false, m0) + fillsgn(m, int2bits((i - 1) / 2))))

Rule argument

seq: ⊦ n ≠ 0 ∧ bits ≠ [] → fillsgn(n, bits + boolvar ') = fillsgn(n -1, bits) + boolvar subst: [boolvar, bits, n] → [i % 2 ≠ 0, int2bits((i - 1) / 2), m + 1] rotate: F spec: bitopsaux inst: name: fill-last

Additional information

Used simplifier rules: ⊦ m + 1 ≠ 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ int2bits(j) ≠ []; Used terms: i % 2 ≠ 0, int2bits((i - 1) / 2), m + 1