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Proof step 63 from proof int2bytes-len-eq-pos (previous step)

int2bytes(i).first = i2b(0), 2 ^ (8 * n→i(# int2bytes(i) - 1) - 1) < 2 ^ ((n→i(n) - 1) * 8), 2 ^ (8 * n→i(# int2bytes(i) - 1) - 1) ≤ i, 1 + (# int2bytes(i) - 1 - 1) < n, 0 ≤ i, 2 ≤ # int2bytes(i), i < 2 ^ (8 * n→i(# int2bytes(i) - 1)), i < 2 ^ ((n→i(n) - 1) * 8), 2 ^ ((n→i(n) - 1) * 8 - 1) ≤ i, n→i(n) ≤ 1 + n→i(# int2bytes(i) - 1) ⊦ # int2bytes(i) = n, int2bytes(i).rest = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ n ≤ m → n→i(m - n) = n→i(m) - n→i(n) subst: [n, m] → [1, # int2bytes(i)] rotate: F spec: intnat inst: name: n2i-sub

Additional information

Used simplifier rules: int2bytes-empty: ⊦ int2bytes(i) ≠ [];%int2bytes-empty: ⊦ int2bytes(i) ≠ [];% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + 1 ≤ n ↔ m < n;% ⊦ i ≥ 0 → ((* i) + n→i(n) ≤ n→i(m) ↔ i→n(i) + n ≤ m);% ⊦ 0 < n ↔ n ≠ 0;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → n ≠ 0;% ⊦ m < 1 ↔ m = 0;% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward)% ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ m ≠ n → (m ≤ n ↔ m < n);% ⊦ n→i(m) ≤ n→i(n) ↔ m ≤ n;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + (j - i) = j;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ # bytes = 0 ↔ bytes = [];% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);%0 ≤ i ⊦ (* i) < n→i(n) ↔ i→n(i) < n;% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;%0 ≤ j ⊦ 2 ^ j < 2 ^ j0 ↔ j < j0;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i < j + 1 ↔ i ≤ j;% ⊦ 0 < i → (i * j ≤ i * i0 ↔ j ≤ i0);% ⊦ i - j ≤ i0 ↔ i ≤ j + i0;% ⊦ m < n → ¬ n < m; Used terms: 1, # int2bytes(i)