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

¬ 0 < j, 0 ≤ i0, # int2bits(j) ≤ i→n(i0) + 1 ⊦ cast(i0 + 1, j) = j, ¬ 2 ^ i0 ≤ j ∧ ¬ 2 ^ i0 + j < 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
2 ^ i0 + j < 0, j ≤ 0, j < 2 ^ i0, # int2bits(j) ≤ i→n(i0) + 1, 0 ≤ i0 ⊦ cast(i0 + 1, j) = j

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ 0 ≤ i → ¬ 2 ^ i ≤ 0;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ ¬ i < j ↔ j ≤ i;