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Proof step 32 from proof cast-mod-pos-low (previous step)

i→n(i) + 1 ≤ # int2bits(j % 2 ^ i), j % 2 ^ i < i, j % 2 ^ i ≤ 0, 2 ^ i ≤ j, 0 ≤ 2 ^ (i - 1) + j, j % 2 ^ i < j, 2 ^ (i - 1) ≤ j, 0 ≤ j, 0 < i, j % 2 ^ i < 2 ^ (i - 1), i→n(i) ≤ (# int2bits(j % 2 ^ i) - 1) + # int2bits(j / 2 ^ i), i→n(i) + 1 < # int2bits(j % 2 ^ i) ⊦ bits2int(lastn(i→n(i), int2bits(j / 2 ^ i) + int2bits(j % 2 ^ i).rest)) = j % 2 ^ i, int2bits(j % 2 ^ i) = [], i→n(i) = # int2bits(j % 2 ^ i) - 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
j % 2 ^ i < i, j % 2 ^ i ≤ 0, 2 ^ i ≤ j, 0 ≤ 2 ^ (i - 1) + j, j % 2 ^ i < j, 2 ^ (i - 1) ≤ j, 0 ≤ j, 0 < i, j % 2 ^ i < 2 ^ (i - 1), i→n(i) ≤ (# int2bits(j % 2 ^ i) - 1) + # int2bits(j / 2 ^ i), i→n(i) + 1 < # int2bits(j % 2 ^ i), i→n(i) < # int2bits(j % 2 ^ i) ⊦ bits2int(lastn(i→n(i), int2bits(j / 2 ^ i) + int2bits(j % 2 ^ i).rest)) = j % 2 ^ i, i→n(i) = # int2bits(j % 2 ^ i) - 1

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + 1 ≤ n ↔ m < n;% ⊦ int2bits(j) ≠ [];