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Proof step 6 from proof bits2int-le8 (previous step)

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) ⊦ i = ~1, bits = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
bits2int(bits) < i, bits2int(bits) < 2 ^ i, 0 < 2 ^ i, bits2int(bits) + 1 < 2 ^ i, bits2int(bits) < 2 ^ i * 2, bits2int(bits) + 1 < 2 ^ i * 2, 0 ≤ bits2int(bits) + 2 ^ i * 2, 0 ≤ i, bits2int(bits) + 2 ^ i < 0, # bits ≤ 8, bits2int(bits) < ~128, bits2int(bits) + 2 ^ i < i, bits2int(bits) < ~1, bits2int(bits) < 0 ⊦ bits = [], i = ~1

Rule argument

Additional information

Used simplifier rules: ⊦ i + j < i0 ∧ ¬ j < j0 → i + j0 < i0;% ⊦ i < i + j ↔ 0 < j;% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ i + j < j ↔ i < 0;% ⊦ i +1 = i + 1;% ⊦ i + j < i + i0 ↔ j < i0;% ⊦ i < j ∧ j < j0 → i < j0; (forward)% ⊦ i < j ∧ j < i0 → i +1 < i0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ 0 < i → (i < i * j ↔ 1 < j);% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 1 * i = i;% ⊦ i + j < (* i1) * i ↔ j < (i1 - 1) * i;% ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;