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Proof step 16 from proof cast-mult-add-h (previous step)

j + 1 < 0 ∧ j0 - 2 ^ i < 0 ∧ 0 < i, 0 ≤ i, 0 < i, j0 < 2 ^ i, j < 0, 0 ≤ j0 ⊦ cast(i, j0 - 2 ^ i) = cast(i, j0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
0 ≤ i, 0 < i, j < 0, 0 ≤ j0, j < ~1, j0 < 2 ^ i ⊦ cast(i, j0 - 2 ^ i) = cast(i, j0)

Rule argument

Additional information

Used simplifier rules: ⊦ i + 0 = i;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;