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Proof step 14 from proof cast-mod-pos-low (previous step)

¬(2 ^ i ≤ j ∧ 0 < i), 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), int2bits(j))) = j % 2 ^ i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
j < 2 ^ i, 0 ≤ 2 ^ (i - 1) + j, j % 2 ^ i < j, 2 ^ (i - 1) ≤ j, 0 ≤ j, 0 < i, j % 2 ^ i < 2 ^ (i - 1), i→n(i) ≤ # int2bits(j), 0 ≤ i ⊦ bits2int(lastn(i→n(i), int2bits(j))) = j % 2 ^ i

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ 2 ^ (i - 1) < 2 ^ i ↔ 0 ≤ i;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;