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Proof step 6 from proof cast-size-fits (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
n→i(# int2bits(j)) ≤ i0 + 1, 0 ≤ i0 ⊦ cast(i0 + 1, j) = j, ¬ 2 ^ i0 ≤ j ∧ ¬ 2 ^ i0 + j < 0

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;