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Proof step 56 from proof int2bytes-len-eq-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 57:
int2bytes(i).first = i2b(0), 1 + (# int2bytes(i).rest - 1) < n, n→i(n) ≤ 1 + n→i(# int2bytes(i) - 1), 2 ^ (8 * (1 + n→i(# int2bytes(i).rest - 1)) - 1) ≤ i, 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 ⊦ # int2bytes(i) = n, int2bytes(i).rest = []

Rule argument

Additional information

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