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Proof step 27 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 ⊦ 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 28:
⊦ ¬ bits.first ∧ bits ≠ [] → bits2int(bits) = bits2uint(bits)
Proof step 29:
¬ ( ¬ firstn(# int2bits((i - 1) / 2), mklist(false, m) + int2bits((i - 1) / 2)).first ∧ firstn(# int2bits((i - 1) / 2), mklist(false, m) + int2bits((i - 1) / 2)) ≠ []), i→n(j) = m + 1, i < ~1, 0 < j, 1 < j, i < 0, n ≤ # int2bits((i - 1) / 2), n ≤ # int2bits((i - 1) / 2) + 1 ⊦ 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)))

Rule argument

seq: ⊦ ¬ bits.first ∧ bits ≠ [] → bits2int(bits) = bits2uint(bits) subst: [bits] → [firstn (# int2bits((i - 1) / 2), mklist(false, m) + int2bits((i - 1) / 2))] rotate: F spec: int2bits inst: name: bits2int-pos-02

Additional information

Used terms: firstn (# int2bits((i - 1) / 2), mklist(false, m) + int2bits((i - 1) / 2))