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Proof step 9 from proof bytes2int-size-04 (previous step)

b2i(by) < 0, 2 ^ (8 * (2 + n→i(# bytes1)) - 1) + 256 * bytes2int(by ' + bytes1) + band(255, b2i(by0)) < 0, ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → b2i(by) < 0 ∧ 2 ^ ((n→i(# bytes0) + 1) * 8 - 1) + bytes2int(by ' + bytes0) < 0 → false ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 10:
8 * (2 + n→i(# bytes1)) - 1 = 8 + (8 * (1 + n→i(# bytes1)) - 1), b2i(by) < 0, 2 ^ (8 * (2 + n→i(# bytes1)) - 1) + 256 * bytes2int(by ' + bytes1) + band(255, b2i(by0)) < 0, ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → b2i(by) < 0 ∧ 2 ^ ((n→i(# bytes0) + 1) * 8 - 1) + bytes2int(by ' + bytes0) < 0 → false ⊦

Rule argument

fma: 8 * (2 + n→i(# bytes1)) - 1 = 8 + (8 * (1 + n→i(# bytes1)) - 1)

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + (j - i0) = i + j - i0;% ⊦ i * j + i = i * (j + 1);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ i + (j - i) = j;% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0); Used formulas: 8 * (2 + n→i(# bytes1)) - 1 = 8 + (8 * (1 + n→i(# bytes1)) - 1)