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Proof step 15 from proof shiftzero-rec-neg-longer (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ n ≤ # bits → fillsgn(n, bits) = bits subst: [bits, n] → [int2bits((i - 1) / 2) + (i % 2 ≠ 0)', n] rotate: F spec: bitopsaux inst: name: fillsgn-longer

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ m < n → n ≠ 0;% ⊦ ¬ m + n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: int2bits((i - 1) / 2) + (i % 2 ≠ 0)', n