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Proof step 53 from proof cast-mod-pos-high (previous step)

0 < j % 2 ^ i, 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, ¬ j % 2 ^ i < 2 ^ (n→i(i→n(i) + 1) - 1) ⊦ 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 closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ 0 < i → ¬ 2 ^ i ≤ j % 2 ^ i;