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Proof step 36 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 ⊦ m0 = 0, i = ~1, j = 0, bits2uint(firstn(m, mklist(false, m0) + mklist(true, m - # int2bits((i - 1) / 2)) + int2bits((i - 1) / 2))) = bits2int(firstn(m, mklist(false, m0) + mklist(true, m - # int2bits((i - 1) / 2)) + int2bits((i - 1) / 2)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ ¬ bits.first ∧ bits ≠ [] → bits2int(bits) = bits2uint(bits)
Proof step 38:
¬ ( ¬ firstn(m, mklist(false, m0) + mklist(true, m - # int2bits((i - 1) / 2)) + int2bits((i - 1) / 2)).first ∧ firstn(m, mklist(false, m0) + mklist(true, m - # int2bits((i - 1) / 2)) + int2bits((i - 1) / 2)) ≠ []), i→n(j) = m0 + 1, # int2bits((i - 1) / 2) ≤ m, i < ~1, i < 0, 1 < j, 0 < j ⊦ m0 = 0, i = ~1, j = 0, bits2uint(firstn(m, mklist(false, m0) + mklist(true, m - # int2bits((i - 1) / 2)) + int2bits((i - 1) / 2))) = bits2int(firstn(m, mklist(false, m0) + mklist(true, m - # int2bits((i - 1) / 2)) + int2bits((i - 1) / 2)))

Rule argument

seq: ⊦ ¬ bits.first ∧ bits ≠ [] → bits2int(bits) = bits2uint(bits) subst: [bits] → [firstn (m, mklist(false, m0) + mklist(true, m - # int2bits((i - 1) / 2)) + int2bits((i - 1) / 2))] rotate: F spec: int2bits inst: name: bits2int-pos-02

Additional information

Used simplifier rules: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: firstn (m, mklist(false, m0) + mklist(true, m - # int2bits((i - 1) / 2)) + int2bits((i - 1) / 2))