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Proof step 52 from proof uint2bits-add-low (previous step)

j0 < 2 ^ (i2 + 2), 0 ≤ (i1 * 2 + j0) + 2 ^ (i2 + 2), 0 ≤ 2 ^ (1 + i2) + i1 * 2 + j0, 0 ≤ 2 * (i1 + 1) + j0 + i2, 0 < 2 * (i1 + 1) + j0 + i2, 0 ≤ 2 ^ (i2 + 2), 0 ≤ 2 * (i1 + 1) + i2, 0 ≤ (i1 * 2 + j0) + j0, 0 < (i1 * 2 + j0) + j0, 1 < i1 * 2 + j0, 0 ≤ i1, j0 < 2, 0 ≤ j0, 2 ^ i2 < i1, i1 * 2 + j0 ≤ 2 ^ (i2 + 2) + 1, 2 < (i1 * 2 + j0) + 2 ^ (i2 + 2), i1 * 2 + j0 ≤ 2 ^ (i2 + 2), 2 < 2 ^ (1 + i2) + i1 * 2 + j0, i1 * 2 + j0 ≤ 1 + 2 ^ (1 + i2), ~2 < i2, 2 < 2 * (i1 + 1) + j0 + i2, i1 * 2 + j0 < 2 ^ (i2 + 2), 0 ≤ 2 ^ (1 + i2), 1 < (i1 * 2 + j0) + j0, 0 < i1 * 2 + j0, j0 + 1 < 2 ^ (i2 + 2), 0 < 2 ^ (i2 + 2), 0 < 2 ^ (1 + i2), 2 < 2 ^ (i2 + 2), 1 < 2 ^ (1 + i2) + i1 * 2, 1 < 2 * (i1 + 1) + i2, 0 < 2 ^ (1 + i2) + i1 * 2, 0 < 2 * (i1 + 1) + i2, ∀ i0, j. i→n(i0) < i→n(i2 + 2) → true → j < 0 ∧ 0 < i0 ∧ abs(j) ≤ 2 ^ (i0 - 1) → uint2bits(j + 2 ^ i0) = false ' + fillsgn(i→n(i0), int2bits(j)) ⊦ uint2bits(2 ^ (1 + i2) - i1) + (~1 = (1 - i1 * 2 + j0) % 2)' = false ' + fillsgn(i→n(i2 + 2), int2bits(1 - i1 * 2 + j0)), 1 = i1 * 2 + j0, ~1 = i2

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j subst: [i, j] → [i2, 2] rotate: F spec: int-pot inst: name: succ

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < 0 → 2 ^ i = 0;% ⊦ i < 0 → (~2 < i ↔ i = ~1);% ⊦ i + j = j + i; Used terms: i2, 2