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Proof step 18 from proof fix-butlast-longer (previous step)

fillsgn(n, by0 ' + bytes1) = by ' + bytes0, 1 + # bytes1 < n ⊦ (¬ 0 ≤ b2i(by0) ⊃ i2b(~1);i2b(0)) = by, bytes1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: fillsgn-neg rotate: F subst: [bytes, n] → [by0 ' + bytes1, n]

Additional information

Used simplifier rules: bytes2int-neg-01: ⊦ bytes2int(by ' + bytes) < 0 ↔ b2i(by) < 0;% ⊦ #(bytes + bytes0) = # bytes + # bytes0;% ⊦ # by ' = 0 +1;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ by ' + bytes = bytes0 → by ∈ bytes0; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ by ∈ bytes + bytes0 ↔ ¬ ¬(by ∈ bytes ∨ by ∈ bytes0);% ⊦ by ∈ by0 ' ↔ by = by0;% ⊦ by ∈ mklist(by0, n) → by = by0; (forward)%⊦ ¬ by ∈ bytes → ( bytes + by0 ' + bytes0 = by ' + bytes1 ↔ bytes = [] ∧ by0 = by ∧ bytes0 = bytes1);% ⊦ mklist(by, m) = [] ↔ m = 0;% ⊦ m + n = n + m;% ⊦ n < m → m - n ≠ 0; Used terms: by0 ' + bytes1, n