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Proof step 9 from proof cast-size-fits (previous step)

0 ≤ i0 + 1, # int2bits(j) ≤ i→n(i0 + 1), 0 ≤ i0 ⊦ 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 10:
0 ≤ i0, # int2bits(j) ≤ i→n(i0) + 1 ⊦ cast(i0 + 1, j) = j, ¬ 2 ^ i0 ≤ j ∧ ¬ 2 ^ i0 + j < 0

Rule argument

Additional information

Used simplifier rules: ⊦ 0 ≤ i → i→n(i + 1) = i→n(i) + 1;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;