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Proof step 63 from proof cast-mod-pos-high (previous step)

0 < j % 2 ^ i, 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 + (j % 2 ^ i - 2 ^ (n→i(# uint2bits(j % 2 ^ i)) - 1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 64:
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, 0 < j % 2 ^ i ⊦ 2 ^ i = 2 ^ (n→i(# uint2bits(j % 2 ^ i)) - 1)

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i + j = i + i0 ↔ j = i0;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + (j - i0) = i + j - i0;