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Proof step 54 from proof int2bytes-len-eq-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 55:
⊦ n ≤ m → n→i(m - n) = n→i(m) - n→i(n)

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