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Proof step 4 from proof bytes2int-size-04 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 1 < # bytes → bytes2int(bytes) = bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255)
Proof step 6:
1 < #(by ' + bytes), 2 ^ ((n→i(# bytes) + 1) * 8 - 1) + bytes2int((by ' + bytes).butlast) * 256 + band(b2i((by ' + bytes).last), 255) < 0, b2i(by) < 0, ∀ by, bytes0. # bytes0 < # bytes → b2i(by) < 0 ∧ 2 ^ ((n→i(# bytes0) + 1) * 8 - 1) + bytes2int(by ' + bytes0) < 0 → false ⊦

Rule argument

name: bytes2int-rec-01 rotate: F subst: [bytes] → [by ' + bytes]

Additional information

Used simplifier rules: bytes2int-one: ⊦ bytes2int(by ') = b2i(by);% ⊦ #(bytes + bytes0) = # bytes + # bytes0;% ⊦ # by ' = 0 +1;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);% ⊦ m + 1 ≠ 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ 1 = m + 1 ↔ m = 0;% ⊦ # bytes = 0 ↔ bytes = [];% ⊦ bytes + [] = bytes;% ⊦ # [] = 0;% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ ¬ b2i(by) < ~128;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: by ' + bytes