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Proof step 17 from proof shiftzero-rec-neg-shorter (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ j < ~1 → int2bits(j) = int2bits((j - 1) / 2) + int2bits(j % 2) subst: [j] → [i] rotate: F spec: int2bits inst: name: int2bits-rec-neg-01

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m + m0 ≤ m ↔ m0 = 0;% ⊦ # bits = 0 ↔ bits = [];% ⊦ int2bits(j) ≠ [];% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: i