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Proof step 4 from proof bits2int-le8-01 (previous step)

0 < bits2int(bits) → (∃ i. 0 ≤ i ∧ 2 ^ i ≤ bits2int(bits) ∧ bits2int(bits) < 2 ^ (i + 1)), 127 < bits2int(bits), # bits ≤ 8, 0 < bits2int(bits), 0 ≤ bits2int(bits) ⊦ bits = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
bits2int(bits) < 2 ^ i * 2, 2 ^ i ≤ bits2int(bits), # bits ≤ 8, 127 < bits2int(bits), 64 < 2 ^ i, 63 < 2 ^ i, 64 < bits2int(bits), 63 < bits2int(bits), 0 < 2 ^ i, 0 ≤ 2 ^ i, 32 < 2 ^ i, 31 < 2 ^ i, 0 < bits2int(bits), 32 < bits2int(bits), 31 < bits2int(bits), 16 < 2 ^ i, 15 < 2 ^ i, 16 < bits2int(bits), 15 < bits2int(bits), 8 < 2 ^ i, 7 < 2 ^ i, 8 < bits2int(bits), 7 < bits2int(bits), 4 < 2 ^ i, 3 < 2 ^ i, 4 < bits2int(bits), 3 < bits2int(bits), 1 < i, 0 < i, 0 ≤ i, 1 < bits2int(bits), 1 < 2 ^ i ⊦ 0 = bits2int(bits), bits = []

Rule argument

Additional information

Used simplifier rules: ⊦ 0 ≤ i → (2 < 2 ^ i ↔ 1 < i);% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ (* i) < j ∧ 0 < i → 0 ≤ j ∧ 0 < j; (forward)% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ 0 < i ∧ 0 ≤ j → ((* j) < (* i) * i0 ↔ j / i < i0);% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 1 * i = i;% ⊦ j < (* i1) * j ↔ 0 < (i1 - 1) * j;% ⊦ i < j ∧ j < j0 → i < j0; (forward)% ⊦ i < j ∧ j < i0 → i +1 < i0; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j ∧ i = i0 → i0 < j; (forward)% ⊦ i < j ∧ j = i0 → i < i0; (forward)% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ ¬ i < j ↔ j ≤ i;