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Proof step 14 from proof cast-size-fits-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
0 < i, 0 ≤ i, 0 ≤ 2 ^ (i - 1), i→n(i) < # int2bits(~1) ⊦ cast(i, ~1) = ~1, # int2bits(~1) = 1

Rule argument

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ [];% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n → n ≠ 0; (forward)% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;%i < 0 ⊦ (* i) + j = j - ~ i;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ ~1 < i ↔ 0 ≤ i;