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Proof step 4 from proof bits2int-le8 (previous step)

bits2int(bits) < 0 → (∃ i. ~1 ≤ i ∧ bits2int(bits) < ~(2 ^ i) ∧ ~(2 ^ (i + 1)) ≤ bits2int(bits)), bits2int(bits) < ~128, # bits ≤ 8, bits2int(bits) < 0 ⊦ bits = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
bits2int(bits) + 2 ^ i < 2 ^ (i + 1), 0 < 2 ^ (i + 1), 2 ^ i < 2 ^ (i + 1), bits2int(bits) < ~128, # bits ≤ 8, bits2int(bits) < 0, bits2int(bits) + 2 ^ i < 0, ~1 ≤ i, 0 ≤ 2 ^ (i + 1) + bits2int(bits), bits2int(bits) + 1 < 2 ^ (i + 1), bits2int(bits) < 2 ^ (i + 1), (bits2int(bits) + 2 ^ i) + 1 < 2 ^ (i + 1) ⊦ bits = []

Rule argument

Additional information

Used simplifier rules: ⊦ i +1 = i + 1;% ⊦ i < j ∧ j < j0 → i < j0; (forward)% ⊦ i < j ∧ j < i0 → i +1 < i0; (forward)% ⊦ i < i + j ↔ 0 < j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j < i + i0 ↔ j < i0;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;% ⊦ i < ~ j ↔ i + j < 0;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;