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Proof step 9 from proof uint2bits-mod2pot (previous step)

0 < j, 2 ^ i < j, 0 ≤ i, ∀ 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)) ⊦ j = 1, uint2bits(j % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j / 2).rest + (j % 2 = 1)'))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
0 < n ⊦ lastn((* n), bits + boolvar ') = lastn(n -1, bits) + boolvar '
Proof step 11:
¬ 0 < i→n(i), 0 < j, 2 ^ i < j, 0 ≤ i, ∀ 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)) ⊦ j = 1, uint2bits(j % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j / 2).rest + (j % 2 = 1)'))
Proof step 12:
0 < i→n(i), 0 < j, 2 ^ i < j, 0 ≤ i, ∀ 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)) ⊦ j = 1, uint2bits(j % 2 ^ i) = sgn(false ' + lastn(i→n(i) -1, uint2bits(j / 2).rest) + (j % 2 = 1)')

Rule argument

seq: 0 < n ⊦ lastn((* n), bits + boolvar ') = lastn(n -1, bits) + boolvar ' subst: [boolvar, bits, n] → [j % 2 = 1, uint2bits(j / 2).rest, i→n(i)] rotate: F spec: list-del inst: bitlista name: num-lastN

Additional information

Used terms: j % 2 = 1, uint2bits(j / 2).rest, i→n(i)