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Proof step 10 from proof int2bits-lelen (previous step)

0 ≤ i1 ∧ 2 ^ i1 ≤ i ∧ i < 2 ^ (i1 + 1), n→i(m) = i0 + 1, i < 2 ^ i1 * 2, 2 ^ i1 ≤ i, 0 ≤ i1, 0 < 2 ^ i1, 0 < i ⊦ i = 0, i→n(i1 + 2) ≤ m ↔ ¬ 2 ^ i0 ≤ i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
0 ≤ i ⊦ i→n(i) ≤ m ↔ i ≤ n→i(m)
Proof step 12:
0 ≤ i1 + 2, 0 ≤ i1 ∧ 2 ^ i1 ≤ i ∧ i < 2 ^ (i1 + 1), n→i(m) = i0 + 1, i < 2 ^ i1 * 2, 2 ^ i1 ≤ i, 0 ≤ i1, 0 < 2 ^ i1, 0 < i ⊦ i = 0, i1 + 2 ≤ n→i(m) ↔ ¬ 2 ^ i0 ≤ i

Rule argument

seq: 0 ≤ i ⊦ i→n(i) ≤ (* m) ↔ i ≤ n→i(m) subst: [m, i] → [m, i1 + 2] rotate: F spec: intnat inst: name: num-i2n-le

Additional information

Used simplifier rules: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ i * j = j * i;% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i < j ∧ j < i0 → i +1 < i0; (forward)% ⊦ i < j ∧ j < j0 → i < j0; (forward)%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; Used terms: m, i1 + 2