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Proof step 17 from proof uint2bits-add-low-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ j < 0 ∧ 0 < i ∧ abs(j) ≤ 2 ^ (i - 1) → uint2bits(j + 2 ^ i) = false ' + fillsgn(i→n(i), int2bits(j))
Proof step 19:
j0 < 0 ∧ 0 < i ∧ abs(j0) ≤ 2 ^ (i - 1), j0 < 0, 0 < i, 0 ≤ j0 + 2 ^ (i - 1), 0 ≤ 2 ^ i + j0, 0 ≤ i, 1 < j, 0 < j ⊦ j = 1, fillsgn(i→n(i) + 1, false ' + fillsgn(i→n(i), int2bits(j0))).rest = fillsgn(i→n(i), int2bits(j0))

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 ↔ i = j);% ⊦ i < 0 → abs(i) = ~ i;% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ fillsgn(0, bits) = bits;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ i < 0 → (~1 ≤ i ↔ i = ~1);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + 0 = i;% ⊦ i < 0 ∧ 0 < j → ¬ j ≤ i;% ⊦ i + j = j + i; Used terms: j0, i