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Proof step 10 from proof fix-rec-neg (previous step)

b2i(by) < 0, 1 + # bytes0 < n, bytes2int(by ' + bytes0) < 0 ⊦ mklist(i2b(~1), n - 1 + # bytes0) + by ' + bytes0 = i2b(~1) ' + fix(n - 1, by ' + bytes0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ # bytes ≤ n ∧ bytes2int(bytes) < 0 → fix(n, bytes) = mklist(i2b(~1), n - # bytes) + bytes
Proof step 12:
#(by ' + bytes0) ≤ n - 1 ∧ bytes2int(by ' + bytes0) < 0, b2i(by) < 0, 1 + # bytes0 < n, bytes2int(by ' + bytes0) < 0 ⊦ mklist(i2b(~1), n - 1 + # bytes0) + by ' + bytes0 = i2b(~1) ' + mklist(i2b(~1), n - 1 - #(by ' + bytes0)) + by ' + bytes0

Rule argument

name: fix-neg-le rotate: F subst: [bytes, n] → [by ' + bytes0, n - 1]

Additional information

Used simplifier rules: ⊦ #(bytes + bytes0) = # bytes + # bytes0;% ⊦ # by ' = 0 +1;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ m + 1 ≤ n ↔ m < n;% ⊦ m < n → n ≠ 0;% ⊦ m < 1 ↔ m = 0;% ⊦ ¬ m ≤ n ↔ n < m;%n0 ≤ n ⊦ m < n - n0 ↔ m + n0 < n;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m + n = n + m;% ⊦ m < n → (n ≤ m ↔ false);% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: by ' + bytes0, n - 1