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Proof step 50 from proof cast-mod-pos-high (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
i→n(i) ≤ (# fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)) - 1) + # int2bits(j / 2 ^ i), 2 ^ (i - 1) ≤ j % 2 ^ i, 0 < i, 0 ≤ j, 2 ^ (i - 1) ≤ j, 0 ≤ 2 ^ (i - 1) + j, 2 ^ i ≤ j, 2 ^ i ≤ j % 2 ^ i, 0 < j % 2 ^ i, i→n(i) + 1 < # int2bits(j % 2 ^ i) ⊦ i→n(i) = # fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)) - 1, fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)) = [], j % 2 ^ i = 2 ^ i + bits2int(lastn(i→n(i), int2bits(j / 2 ^ i) + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest))

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;