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Proof step 30 from proof shiftzero-rec-neg-longer (previous step)

i→n(j) = m + 1, i < ~1, 0 < j, 1 < j, i < 0, n ≤ # int2bits((i - 1) / 2), n ≤ # int2bits((i - 1) / 2) + 1, firstn(# int2bits((i - 1) / 2), mklist(false, m) + int2bits((i - 1) / 2)).first ⊦ m = 0, j = 0, i = ~1, bits2uint(firstn(# int2bits((i - 1) / 2), mklist(false, m) + int2bits((i - 1) / 2))) = bits2int(firstn(# int2bits((i - 1) / 2), mklist(false, m) + int2bits((i - 1) / 2)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ n ≠ 0 ∧ bits ≠ [] → (firstn(n, bits).first ↔ bits.first)

Rule argument

seq: ⊦ n ≠ 0 ∧ bits ≠ [] → (firstn(n, bits).first ↔ bits.first) subst: [bits, n] → [mklist(false, m) + int2bits((i - 1) / 2), # int2bits((i - 1) / 2)] rotate: F spec: list-del inst: bitlista name: firstn-first

Additional information

Used simplifier rules: ⊦ n ≠ 0 → ((mklist(boolvar, n) + bits).first ↔ boolvar);% ⊦ # bits = 0 ↔ bits = [];% ⊦ int2bits(j) ≠ [];% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: mklist(false, m) + int2bits((i - 1) / 2), # int2bits((i - 1) / 2)