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Proof step 13 from proof cast-size-fits-01 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 14:
j = ~1, 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

fma: j = ~1

Additional information

Used simplifier rules: cast-zero: ⊦ 0 < i → cast(i, 0) = 0;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j); Used formulas: j = ~1