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Proof step 54 from proof cast-mod-pos-high (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 55:
i→n(i) = # fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, 2 ^ i ≤ j, 0 ≤ 2 ^ (i - 1) + j, 2 ^ (i - 1) ≤ j, 0 ≤ j, 0 < i, 2 ^ (i - 1) ≤ j % 2 ^ i ⊦ j % 2 ^ i = 2 ^ i + bits2int(fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest)

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m ≤ m + n;