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Proof step 12 from proof int2bits-len-range (previous step)

# int2bits(j) = i→n(i0 + 2), 0 ≤ 2 ^ i + j, j < 2 ^ i, 0 ≤ i0, 2 ^ i0 ≤ j, j < 2 ^ i0 * 2, 1 < 2 ^ i, 0 < i, 0 ≤ 2 ^ i, 0 < 2 ^ i, 0 < j, i0 < i, 0 < 2 ^ i0, i→n(i) + 1 < # int2bits(j) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
# int2bits(j) = i→n(i0 + 2), i→n(i) + 1 < i→n(i0 + 2), 0 < 2 ^ i0, i0 < i, 0 < j, 0 < 2 ^ i, 0 ≤ 2 ^ i, 0 < i, 1 < 2 ^ i, j < 2 ^ i0 * 2, 2 ^ i0 ≤ j, 0 ≤ i0, j < 2 ^ i, 0 ≤ 2 ^ i + j ⊦ ~2 = i0

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ m < n → n ≠ 0; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)