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Proof step 20 from proof cast-mod-pos-high (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
0 < j, 2 ^ (i - 2) ≤ j, j < 2 ^ i, 0 ≤ 2 ^ (i - 1) + j, 2 ^ (i - 1) ≤ j, 0 ≤ j, 2 ^ (i - 1) ≤ j % 2 ^ i, 0 ≤ i, 2 ^ (i - 2) < 2 ^ i, 0 < i ⊦ j % 2 ^ i = bits2int(lastn(i→n(i), int2bits(j))) + 2 ^ i, # int2bits(j) = i→n(i) + 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 ∧ j < j0 → i < j0; (forward)% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 < i → n→i(i→n(i)) = i;