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Proof step 8 from proof uint2bits-len-max (previous step)

0 ≤ 2 ^ (i0 + 1), 0 < 2 ^ (i0 + 1), 0 ≤ 2 ^ i, 0 < 2 ^ i, 0 < i, i0 < i, 1 < 2 ^ (i0 + 1), 1 < 2 ^ i, 0 ≤ i, 0 ≤ i0, 2 ^ i0 ≤ j, j < 2 ^ (i0 + 1), i→n(i) + 1 < i→n(i0 + 2), j < 2 ^ i, 0 < j ⊦ 0 = j, ~2 = i0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: 0 ≤ i, 0 ≤ j ⊦ i→n(i + j) = i→n(i) + i→n(j) subst: [j, i] → [2, i0] rotate: F spec: intnat inst: name: add-01

Additional information

Used simplifier rules: ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;%n < n0 ⊦ m + (* n) < m0 + (* n0) ↔ m < m0 + (n0 - n);% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j);% ⊦ 0 ≤ i → abs(i) = i;% ⊦ 0 < j → abs(j) = j;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: 2, i0