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Proof step 42 from proof int2bytes-len-eq-pos (previous step)

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 ↔ ¬ i < 2 ^ ((n→i(n) - 1) * 8 - 1) ∧ ¬ 2 ^ ((n→i(n) - 1) * 8) ≤ i ∧ n ≠ 0, int2bytes(i).rest = []

User applied rule cut formula

And obtained the following new goals

Proof step 43:
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)) ⊦ n = 0, # int2bytes(i) = n ↔ ¬ i < 2 ^ ((n→i(n) - 1) * 8 - 1) ∧ ¬ 2 ^ ((n→i(n) - 1) * 8) ≤ i ∧ n ≠ 0, int2bytes(i).rest = []

Rule argument

fma: n = 0

Additional information

Used simplifier rules: int2bytes-empty: ⊦ int2bytes(i) ≠ [];% ⊦ # bytes = 0 ↔ bytes = [];% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used formulas: n = 0