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Proof step 23 from proof cast-mod-pos-low (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
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) ≤ (# fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)) - 1) + # int2bits(j / 2 ^ i) ⊦ bits2int(lastn(i→n(i), int2bits(j / 2 ^ i) + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest)) = j % 2 ^ i, fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)) = [], i→n(i) = # fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)) - 1

Rule argument

Additional information

Used simplifier rules: ⊦ n -1 = n - 1;