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Proof step 60 from proof cast-mod-pos-high (previous step)

i→n(i) + 1 ≤ # int2bits(j % 2 ^ i), i→n(i) = # 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(int2bits(j % 2 ^ i).rest)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 61:
i→n(i) = # int2bits(j % 2 ^ i).rest, i→n(i) < # 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 ⊦ j % 2 ^ i = 2 ^ i + bits2int(int2bits(j % 2 ^ i).rest)

Rule argument

Additional information

Used simplifier rules: ⊦ # bits.rest < # bits ↔ bits ≠ [];% ⊦ int2bits(j) ≠ [];% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n → n ≠ 0; (forward)% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + 1 ≤ n ↔ m < n;