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Proof step 33 from proof uint2bits-add-high (previous step)

mklist(false, i→n(i) - 1) = [], 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
i→n(i) - 1 = 0, 0 < i, 2 ^ (i - 1) + 2 < 2 ^ i + 2 ^ i, 2 < 2 ^ i + 2 ^ i, 2 ^ (i - 1) + 1 < 2 ^ i, 1 < 2 ^ i, 2 ^ (i - 1) < 2 ^ i, 2 ^ (i - 1) + 2 < 2 ^ i + i, 2 < 2 ^ i + i, 0 ≤ 2 ^ i + 2 ^ i, 0 < 2 ^ i, 0 ≤ 2 ^ i, 0 ≤ 2 ^ i + 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

Rule argument

Additional information

Used simplifier rules: ⊦ boolvar '.last ↔ boolvar;% ⊦ boolvar ' + bits ≠ [];% ⊦ sgn([]) = [];% ⊦ boolvar '.rest = [];% ⊦ sgn(true ' + true ') = true ';% ⊦ [] + bits = bits;% ⊦ boolvar '.butlast = [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + [] = bits;% ⊦ mklist(boolvar, 0) = [];% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ mklist(boolvar, m) = [] ↔ m = 0;