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Proof step 21 from proof cast-law-add-pos-01 (previous step)

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

User applied rule insert equation

And obtained the following new goals

Proof step 22:
0 < i, 0 ≤ i, 0 ≤ i0, 0 ≤ j1, j1 < 2 ^ i, 2 ^ (i - 1) ≤ j1, 0 < i, j0 < 0 ⊦ cast(i, j0 + j1) = cast(i, ~1 * 2 ^ i + j0 + j1)

Rule argument

pos: left 1 flags: discard

Proof step 21 from proof cast-law-add-pos-01 (previous step)

User applied rule insert equation

And obtained the following new goals

Rule argument

Additional information