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Proof step 29 from proof uint2bits-add-high (previous step)

0 ≤ 2 ^ i + i, 0 ≤ 2 ^ i, 0 < 2 ^ i, 0 ≤ 2 ^ i + 2 ^ i, 2 < 2 ^ i + i, 2 ^ (i - 1) + 2 < 2 ^ i + i, 2 ^ (i - 1) < 2 ^ i, 1 < 2 ^ i, 2 ^ (i - 1) + 1 < 2 ^ i, 2 < 2 ^ i + 2 ^ i, 2 ^ (i - 1) + 2 < 2 ^ i + 2 ^ i, 0 < i, ∀ i0, j. i→n(i0) < i→n(i) → true → j < 0 ∧ 0 < i0 ∧ 2 ^ (i0 - 1) < abs(j) ∧ abs(j) ≤ 2 ^ i0 → uint2bits(j + 2 ^ i0) = sgn(int2bits(j).rest) ⊦ false ' + true ' = sgn(sgn(sgn(false ' + (true ' + mklist(false, i→n(i))).butlast + true ').rest).rest), i = 0, (true ' + mklist(false, i→n(i))).last

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ n ≠ 0 → mklist(boolvar, n) = mklist(boolvar, n -1) + boolvar '
Proof step 31:
i→n(i) ≠ 0, 0 ≤ 2 ^ i + i, 0 ≤ 2 ^ i, 0 < 2 ^ i, 0 ≤ 2 ^ i + 2 ^ i, 2 < 2 ^ i + i, 2 ^ (i - 1) + 2 < 2 ^ i + i, 2 ^ (i - 1) < 2 ^ i, 1 < 2 ^ i, 2 ^ (i - 1) + 1 < 2 ^ i, 2 < 2 ^ i + 2 ^ i, 2 ^ (i - 1) + 2 < 2 ^ i + 2 ^ i, 0 < i, ∀ i0, j. i→n(i0) < i→n(i) → true → j < 0 ∧ 0 < i0 ∧ 2 ^ (i0 - 1) < abs(j) ∧ abs(j) ≤ 2 ^ i0 → uint2bits(j + 2 ^ i0) = sgn(int2bits(j).rest) ⊦ false ' + true ' = sgn(sgn(sgn(false ' + (true ' + mklist(false, i→n(i) -1) + false ').butlast + true ').rest).rest), i = 0, (true ' + mklist(false, i→n(i) -1) + false ').last

Rule argument

seq: ⊦ n ≠ 0 → mklist(boolvar, n) = mklist(boolvar, n -1) + boolvar ' subst: [n, boolvar] → [i→n(i), false] rotate: F spec: list-last inst: bitlista name: mk-last-02

Additional information

Used simplifier rules: ⊦ i→n(i) = 0 ↔ i = 0; Used terms: i→n(i), false