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Proof step 18 from proof bytes2int-size (previous step)

bytes2int(i2b(0) ' + by ' + bytes1) < 2 ^ ((n→i(# bytes1) + 1) * 8), b2i(by) < 0, 2 ^ (8 * (1 + n→i(# bytes1))) * 256 ≤ 256 * bytes2int(i2b(0) ' + by ' + bytes1) + band(255, b2i(by0)), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → 2 ^ ((n→i(# bytes0) + 1) * 8) ≤ bytes2int(i2b(0) ' + by ' + bytes0) ∧ b2i(by) < 0 → false ⊦

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 19:
j * i ≤ j * i0 + j0, abs(j0) < j ⊦ i ≤ i0
Proof step 20:
bytes2int(i2b(0) ' + by ' + bytes1) < 2 ^ ((n→i(# bytes1) + 1) * 8), b2i(by) < 0, 2 ^ (8 * (1 + n→i(# bytes1))) * 256 ≤ 256 * bytes2int(i2b(0) ' + by ' + bytes1) + band(255, b2i(by0)), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → 2 ^ ((n→i(# bytes0) + 1) * 8) ≤ bytes2int(i2b(0) ' + by ' + bytes0) ∧ b2i(by) < 0 → false ⊦ 256 * 2 ^ (8 * (1 + n→i(# bytes1))) ≤ 256 * bytes2int(i2b(0) ' + by ' + bytes1) + band(255, b2i(by0)) ∧ abs(band(255, b2i(by0))) < 256

Rule argument

seq: j * i ≤ j * i0 + j0, abs(j0) < j ⊦ i ≤ i0 subst: [j, i, i0, j0] → [256, 2 ^ (8 * (1 + n→i(# bytes1))), bytes2int(i2b(0) ' + by ' + bytes1), band(255, b2i(by0))] rotate: F spec: int-mult inst: name: modlep-01

Additional information

Used simplifier rules: ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ i + j = j + i;% ⊦ i * j = j * i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: 256, 2 ^ (8 * (1 + n→i(# bytes1))), bytes2int(i2b(0) ' + by ' + bytes1), band(255, b2i(by0))