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Proof step 9 from proof cast-mod-pos-low (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
# int2bits(j) < i→n(i), 0 ≤ 2 ^ (i - 1) + j, j % 2 ^ i < j, 2 ^ (i - 1) ≤ j, 0 ≤ j, 0 < i, j % 2 ^ i < 2 ^ (i - 1) ⊦ bits2int(lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))) = j % 2 ^ i, i = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ m < n → n ≠ 0; (forward)% ⊦ ¬ m ≤ n ↔ n < m;