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Proof step 13 from proof bytes2int-rec-first-zero (previous step)

bytes1 = [] ∨ bytes2int(i2b(0) ' + by ' + bytes1) = band(b2i(by), 255) * 256 ^ n→i(# bytes1) + bytes2int(i2b(0) ' + bytes1), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → true → bytes0 = [] ∨ bytes2int(i2b(0) ' + by ' + bytes0) = band(b2i(by), 255) * 256 ^ n→i(# bytes0) + bytes2int(i2b(0) ' + bytes0) ⊦ 256 * bytes2int((i2b(0) ' + by ') + bytes1) = bytes2int(i2b(0) ' + bytes1) * 256 + 256 ^ (n→i(# bytes1) + 1) * band(b2i(by), 255)

User applied rule cut formula

And obtained the following new goals

Proof step 14:
bytes1 = [], bytes1 = [] ∨ bytes2int(i2b(0) ' + by ' + bytes1) = band(b2i(by), 255) * 256 ^ n→i(# bytes1) + bytes2int(i2b(0) ' + bytes1), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → true → bytes0 = [] ∨ bytes2int(i2b(0) ' + by ' + bytes0) = band(b2i(by), 255) * 256 ^ n→i(# bytes0) + bytes2int(i2b(0) ' + bytes0) ⊦ 256 * bytes2int((i2b(0) ' + by ') + bytes1) = bytes2int(i2b(0) ' + bytes1) * 256 + 256 ^ (n→i(# bytes1) + 1) * band(b2i(by), 255)
Proof step 17:
bytes1 = [] ∨ bytes2int(i2b(0) ' + by ' + bytes1) = band(b2i(by), 255) * 256 ^ n→i(# bytes1) + bytes2int(i2b(0) ' + bytes1), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → true → bytes0 = [] ∨ bytes2int(i2b(0) ' + by ' + bytes0) = band(b2i(by), 255) * 256 ^ n→i(# bytes0) + bytes2int(i2b(0) ' + bytes0) ⊦ bytes1 = [], 256 * bytes2int((i2b(0) ' + by ') + bytes1) = bytes2int(i2b(0) ' + bytes1) * 256 + 256 ^ (n→i(# bytes1) + 1) * band(b2i(by), 255)

Rule argument

fma: bytes1 = []

Additional information

Used formulas: bytes1 = []