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Proof step 8 from proof int2bytes-len-le-neg-01 (previous step)

int2bytes(i).first = i2b(~1), ¬ b2i(int2bytes(i).rest.first) < 0 → bytes2int(i2b(~1) ' + int2bytes(i).rest.first ' + int2bytes(i).rest.rest) + 2 ^ (8 * (n→i(# int2bytes(i).rest.rest) + 1) - 1) < 0, ¬ b2i(int2bytes(i).rest.first) < 0 → 0 ≤ 2 ^ ((n→i(# int2bytes(i).rest.rest) + 1) * 8) + bytes2int(i2b(~1) ' + int2bytes(i).rest.first ' + int2bytes(i).rest.rest) ⊦ n ≤ # int2bytes(i) ↔ ¬ 0 ≤ i + 2 ^ (8 * (n→i(n) - 1) - 1)

User applied rule cut formula

And obtained the following new goals

Proof step 9:
¬ b2i(int2bytes(i).rest.first) < 0, int2bytes(i).first = i2b(~1), ¬ b2i(int2bytes(i).rest.first) < 0 → bytes2int(i2b(~1) ' + int2bytes(i).rest.first ' + int2bytes(i).rest.rest) + 2 ^ (8 * (n→i(# int2bytes(i).rest.rest) + 1) - 1) < 0, ¬ b2i(int2bytes(i).rest.first) < 0 → 0 ≤ 2 ^ ((n→i(# int2bytes(i).rest.rest) + 1) * 8) + bytes2int(i2b(~1) ' + int2bytes(i).rest.first ' + int2bytes(i).rest.rest) ⊦ n ≤ # int2bytes(i) ↔ ¬ 0 ≤ i + 2 ^ (8 * (n→i(n) - 1) - 1)
Proof step 39:
int2bytes(i).first = i2b(~1), ¬ b2i(int2bytes(i).rest.first) < 0 → bytes2int(i2b(~1) ' + int2bytes(i).rest.first ' + int2bytes(i).rest.rest) + 2 ^ (8 * (n→i(# int2bytes(i).rest.rest) + 1) - 1) < 0, ¬ b2i(int2bytes(i).rest.first) < 0 → 0 ≤ 2 ^ ((n→i(# int2bytes(i).rest.rest) + 1) * 8) + bytes2int(i2b(~1) ' + int2bytes(i).rest.first ' + int2bytes(i).rest.rest) ⊦ ¬ b2i(int2bytes(i).rest.first) < 0, n ≤ # int2bytes(i) ↔ ¬ 0 ≤ i + 2 ^ (8 * (n→i(n) - 1) - 1)

Rule argument

fma: ¬ b2i(int2bytes(i).rest.first) < 0

Additional information

Used formulas: ¬ b2i(int2bytes(i).rest.first) < 0