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Proof step 26 from proof cast-mod-pos-high (previous step)

0 < j, # int2bits(j) = i→n(i) + 1, 0 ≤ i, 2 ^ (i - 1) ≤ j % 2 ^ i, 0 < i, 0 ≤ j, 2 ^ (i - 1) ≤ j, 0 ≤ 2 ^ (i - 1) + j, j < 2 ^ i ⊦ j % 2 ^ i = (j - 2 ^ (n→i(# uint2bits(j)) - 1)) + 2 ^ i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
# int2bits(j) = i→n(i) + 1, 0 < j, j < 2 ^ i, 0 ≤ 2 ^ (i - 1) + j, 2 ^ (i - 1) ≤ j, 0 ≤ j, 2 ^ (i - 1) ≤ j % 2 ^ i, 0 ≤ i, 0 < i ⊦ 2 ^ i + j = j % 2 ^ i + 2 ^ (n→i(# uint2bits(j)) - 1)

Rule argument

Additional information

Used simplifier rules: ⊦ 1 < 2 ^ i ↔ 0 < i;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + (j - i0) = i + j - i0;