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

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

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