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Proof step 6 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, (j + 1) * 2 ^ i + (j0 - 2 ^ i)) = cast(i, j0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
0 ≤ j0, j0 < 2 ^ i, 0 < i ⊦ 0 = i, cast(i, j0 - 2 ^ i) = cast(i, j0)

Rule argument

Additional information

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