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Proof step 31 from proof uint2bits-add-high (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
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) ⊦ i = 0, false ' + true ' = sgn(sgn(true ' + (false ' + mklist(false, i→n(i) - 1)).butlast + true ').rest), (false ' + mklist(false, i→n(i) - 1)).last

Rule argument

Additional information

Used simplifier rules: ⊦ (boolvar ' + boolvar0 ' + bits).last ↔ (boolvar0 ' + bits).last;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ (boolvar ' + bits).rest = bits;% ⊦ sgn(false ' + true ' + bits) = false ' + true ' + bits;%⊦ (bits + boolvar ' + bits0).butlast = bits + (boolvar ' + bits0).butlast;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ mklist(boolvar, n) + boolvar ' = boolvar ' + mklist(boolvar, n);% ⊦ n -1 = n - 1;