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Proof step 22 from proof shiftzero-zero-size (previous step)

i < 0 ⊦ j = 0, bits2int(firstn(# int2bits(i), mklist(false, i→n(j)) + int2bits(i))) = bits2uint(firstn(# int2bits(i), mklist(false, i→n(j)) + int2bits(i)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ ¬ bits.first ∧ bits ≠ [] → bits2int(bits) = bits2uint(bits)
Proof step 24:
¬(¬ firstn(# int2bits(i), mklist(false, i→n(j)) + int2bits(i)).first ∧ firstn(# int2bits(i), mklist(false, i→n(j)) + int2bits(i)) ≠ []), i < 0 ⊦ j = 0, bits2int(firstn(# int2bits(i), mklist(false, i→n(j)) + int2bits(i))) = bits2uint(firstn(# int2bits(i), mklist(false, i→n(j)) + int2bits(i)))

Rule argument

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

Additional information

Used terms: firstn(# int2bits(i), mklist(false, i→n(j)) + int2bits(i))