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Proof step 73 from proof uint2bits-mod2pot (previous step)

j % 2 = 0, uint2bits((j / 2) % 2 ^ i0) = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest)), 0 < (j / 2) % 2 ^ i0, 0 ≤ i0, 0 < j, 2 ^ i0 * 2 < j, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ i ∧ 2 ^ i < j0 → uint2bits(j0 % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j0).rest)) ⊦ ~1 = i0, j = 1, true ∈ lastn(i→n(i0), uint2bits(j / 2).rest)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 74:
⊦ ¬ boolvar ∈ bits ↔ mklist(¬ boolvar, # bits) = bits
Proof step 75:
j % 2 = 0, uint2bits((j / 2) % 2 ^ i0) = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest)), 0 < (j / 2) % 2 ^ i0, 0 ≤ i0, 0 < j, 2 ^ i0 * 2 < j, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ i ∧ 2 ^ i < j0 → uint2bits(j0 % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j0).rest)) ⊦ ~1 = i0, j = 1, mklist(¬ true, # lastn(i→n(i0), uint2bits(j / 2).rest)) ≠ lastn(i→n(i0), uint2bits(j / 2).rest)

Rule argument

seq: ⊦ ¬ boolvar ∈ bits ↔ mklist(¬ boolvar, # bits) = bits subst: [bits, boolvar] → [lastn(i→n(i0), uint2bits(j / 2).rest), true] rotate: F spec: bitlista inst: name: mklist-intro

Additional information

Used terms: lastn(i→n(i0), uint2bits(j / 2).rest), true