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Proof step 29 from proof shiftright-rec-pos (previous step)

mklist(false, i→n(i0)) + false ' = false ' + bits, 0 ≤ i0 ⊦ bits2int(firstn(2, mklist(false, i→n(i0)) + false ' + false ' + true ')) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
n ≠ 0 ⊦ firstn((* n), bits) = bits.first ' + firstn(n -1, bits.rest)
Proof step 31:
2 ≠ 0, mklist(false, i→n(i0)) + false ' = false ' + bits, 0 ≤ i0 ⊦ bits2int((mklist(false, i→n(i0)) + false ' + false ' + true ').first ' + firstn(2 -1, (mklist(false, i→n(i0)) + false ' + false ' + true ').rest)) = 0

Rule argument

seq: n ≠ 0 ⊦ firstn((* n), bits) = bits.first ' + firstn(n -1, bits.rest) subst: [bits, n] → [mklist(false, i→n(i0)) + false ' + false ' + true ', 2] rotate: F spec: list-del inst: bitlista name: first-num

Additional information

Used terms: mklist(false, i→n(i0)) + false ' + false ' + true ', 2