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Proof step 12 from proof cast-size-fits-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
0 ≤ 2 ^ (i - 1), j < i, j ≤ 0, 0 ≤ i, j < 2 ^ (i - 1), 0 < i, 0 ≤ 2 ^ (i - 1) + j, i→n(i) < # int2bits(j), ~1 ≤ j ⊦ # int2bits(j) = 1, cast(i, j) = j

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ ¬ i < j ↔ j ≤ i;