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Proof step 32 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) ⊦ 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 weak cut applied rule cut formula

And obtained the following new goals

Proof step 33:
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

Rule argument

fma: mklist(false, i→n(i) - 1) = []

Additional information

Used simplifier rules: ⊦ mklist(boolvar, m) = [] ↔ m = 0;%⊦ m ≠ 0 → (bits + mklist(boolvar, m)).butlast = bits + mklist(boolvar, m - 1);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ sgn(true ' + false ' + bits) = true ' + false ' + bits;% ⊦ (boolvar ' + bits).rest = bits;% ⊦ sgn(false ' + mklist(false, n) + bits) = sgn(false ' + bits);% ⊦ sgn(false ' + true ') = false ' + true ';% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1; Used formulas: mklist(false, i→n(i) - 1) = []