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Proof step 23 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 ⊦ j = 0, i = ~1, bits2uint(firstn(# int2bits((i - 1) / 2), mklist(false, m) + int2bits((i - 1) / 2) + (i % 2 ≠ 0)')) = 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 24:
⊦ n < # bits → firstn(n, bits) = firstn(n, bits.butlast)
Proof step 25:
# int2bits((i - 1) / 2) < #(mklist(false, m) + int2bits((i - 1) / 2) + (i % 2 ≠ 0)'), i→n(j) = m + 1, i < ~1, 0 < j, 1 < j, i < 0, n ≤ # int2bits((i - 1) / 2), n ≤ # int2bits((i - 1) / 2) + 1 ⊦ j = 0, i = ~1, bits2uint(firstn(# int2bits((i - 1) / 2), (mklist(false, m) + int2bits((i - 1) / 2) + (i % 2 ≠ 0)').butlast)) = bits2int(firstn(# int2bits((i - 1) / 2), mklist(false, m) + int2bits((i - 1) / 2)))

Rule argument

seq: ⊦ n < # bits → firstn(n, bits) = firstn(n, bits.butlast) subst: [bits, n] → [mklist(false, m) + int2bits((i - 1) / 2) + (i % 2 ≠ 0)', # int2bits((i - 1) / 2)] rotate: F spec: list-del inst: bitlista name: firstn-butlast-intro

Additional information

Used simplifier rules: ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # mklist(boolvar, n) = n;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ ¬ m + n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: mklist(false, m) + int2bits((i - 1) / 2) + (i % 2 ≠ 0)', # int2bits((i - 1) / 2)