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Proof step 5 from proof bits2int-nls (previous step)

2 ^ n→i(# bits) + bits2int(bits) < 0, ¬ abs(bits2int(bits)) ≤ 2 ^ n→i(# bits) → 2 + # bits ≤ # int2bits(~ bits2int(bits)) ⊦ bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ j < 0 → abs(j) = 0 - j
Proof step 7:
bits2int(bits) < 0, 2 ^ n→i(# bits) + bits2int(bits) < 0, ¬ 0 - bits2int(bits) ≤ 2 ^ n→i(# bits) → 2 + # bits ≤ # int2bits(~ bits2int(bits)) ⊦ bits = []

Rule argument

seq: ⊦ j < 0 → abs(j) = 0 - j subst: [j] → [bits2int(bits)] rotate: F spec: int-abs inst: name: Abs-neg

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 ≤ i → abs(i) = i;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ i + j < j ↔ i < 0;% ⊦ ¬ 2 ^ i < 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ i ≤ j ↔ j < i; Used terms: bits2int(bits)