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Proof step 7 from proof uint2bits-add-high (previous step)

2 ^ (i - 1) + j < 2 ^ i, j + 1 < i, 0 < 2 ^ i, 2 ^ (i - 1) + j < i, (2 ^ (i - 1) + j) + 1 < i, 2 ^ (i - 1) < 2 ^ i, j < 0, 0 < i, 2 ^ (i - 1) + j < 0, 0 ≤ j + 2 ^ i, j < i, j + 1 < 2 ^ i, j < 2 ^ i, (2 ^ (i - 1) + j) + 1 < 2 ^ 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) ⊦ j + 2 ^ i ≠ 1, uint2bits(j + 2 ^ i) = sgn(int2bits(j).rest)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
j + 2 ^ i = 1, (2 ^ (i - 1) + j) + 1 < 2 ^ i, j < 2 ^ i, j + 1 < 2 ^ i, j < i, 2 ^ (i - 1) + j < 0, 0 < i, j < 0, 2 ^ (i - 1) < 2 ^ i, (2 ^ (i - 1) + j) + 1 < i, 2 ^ (i - 1) + j < i, 0 < 2 ^ i, j + 1 < i, 2 ^ (i - 1) + j < 2 ^ i, 2 ^ (i - 1) + j ≤ 0, j ≤ 0, ∀ 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(int2bits(j).rest)

Rule argument

Additional information

Used simplifier rules: uint2bits-one: ⊦ uint2bits(1) = false + true;% ⊦ i < 1 ↔ i ≤ 0;% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ 0 ≤ i ∧ i ≤ 1 → i = 0 ∨ i = 1; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;