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Proof step 5 from proof uint2bits-add-high-02 (previous step)

0 ≤ j0 + 2 ^ i, 2 ^ (i - 1) + j0 < 0, 0 < i, j0 < 0 ⊦ uint2bits(2 ^ i + j0) = sgn(false ' + fillsgn(i→n(i), int2bits(j0).rest))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ j < 0 ∧ 0 < i ∧ 2 ^ (i - 1) < abs(j) ∧ abs(j) ≤ 2 ^ i → uint2bits(j + 2 ^ i) = sgn(int2bits(j).rest)
Proof step 7:
j0 < 0 ∧ 0 < i ∧ 2 ^ (i - 1) < abs(j0) ∧ abs(j0) ≤ 2 ^ i, 0 ≤ j0 + 2 ^ i, 2 ^ (i - 1) + j0 < 0, 0 < i, j0 < 0 ⊦ sgn(int2bits(j0).rest) = sgn(false ' + fillsgn(i→n(i), int2bits(j0).rest))

Rule argument

name: uint2bits-add-high rotate: F subst: [j, i] → [j0, i]

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i < 0 → abs(i) = ~ i;% ⊦ i < ~ j ↔ i + j < 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i + j = j + i; Used terms: j0, i