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Proof step 20 from proof cast-law-mult-pos (previous step)

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

User applied rule insert equation

And obtained the following new goals

Proof step 21:
0 ≤ j, j < 2 ^ i, 2 ^ (i - 1) ≤ j, 0 < i, 0 ≤ i0, 0 ≤ i, 0 < j ⊦ cast(i, j * j0) = cast(i, ~ j0 * 2 ^ i + j * j0)

Rule argument

pos: left 1 flags: discard

Proof step 20 from proof cast-law-mult-pos (previous step)

User applied rule insert equation

And obtained the following new goals

Rule argument

Additional information