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Proof step 4 from proof uint2bits-add-low-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ j < 0 ∧ 0 < i ∧ abs(j) ≤ 2 ^ (i - 1) → uint2bits(j + 2 ^ i) = false ' + fillsgn(i→n(i), int2bits(j))

Rule argument

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

Additional information

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