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Proof step 57 from proof cast-mod-pos-high (previous step)

¬ i→n(i) + 1 ≤ # int2bits(j % 2 ^ i), 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 58:
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, # int2bits(j % 2 ^ i) ≤ i→n(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 < n ↔ n ≤ m;% ⊦ m + 1 ≤ n ↔ m < n;