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Proof step 30 from proof no-leading-zero (previous step)

int2bytes(bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)) = i2b(0) ' + by ' + bytes1 + by0 ', bytes2int(i2b(0) ' + by ' + bytes1) ≤ 0, 0 ≤ band(b2i(by0), 255), 0 ≤ b2i(by), band(b2i(by0), 255) < 256, ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 31:
bytes2int(i2b(0) ' + by ' + bytes1) < 0, int2bytes(bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)) = i2b(0) ' + by ' + bytes1 + by0 ', bytes2int(i2b(0) ' + by ' + bytes1) ≤ 0, 0 ≤ band(b2i(by0), 255), 0 ≤ b2i(by), band(b2i(by0), 255) < 256, ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦
Proof step 34:
int2bytes(bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)) = i2b(0) ' + by ' + bytes1 + by0 ', bytes2int(i2b(0) ' + by ' + bytes1) ≤ 0, 0 ≤ band(b2i(by0), 255), 0 ≤ b2i(by), band(b2i(by0), 255) < 256, ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦ bytes2int(i2b(0) ' + by ' + bytes1) < 0

Rule argument

fma: bytes2int(i2b(0) ' + by ' + bytes1) < 0

Additional information

Used formulas: bytes2int(i2b(0) ' + by ' + bytes1) < 0