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Proof step 11 from proof cast-law-add-pos (previous step)

(i0 * 2 ^ i + j1) + j0 = i0 * 2 ^ i + j1 + j0, 0 ≤ j1, j1 < 2 ^ i, j1 < 2 ^ (i - 1), 0 ≤ j0, 0 ≤ i, 0 ≤ i0, 0 < i ⊦ cast(i, (i0 * 2 ^ i + j1) + j0) = cast(i, j1 + j0)

User applied rule insert equation

And obtained the following new goals

Proof step 12:
0 ≤ j1, j1 < 2 ^ i, j1 < 2 ^ (i - 1), 0 ≤ j0, 0 ≤ i, 0 ≤ i0, 0 < i ⊦ cast(i, i0 * 2 ^ i + j1 + j0) = cast(i, j1 + j0)

Rule argument

pos: left 1 flags: discard

Proof step 11 from proof cast-law-add-pos (previous step)

User applied rule insert equation

And obtained the following new goals

Rule argument

Additional information