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Proof step 22 from proof cast-law-add-pos (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
j0 + j1 = i1 + 2 ^ i, 0 ≤ i, 0 ≤ i0, 0 ≤ j1, j1 < 2 ^ i, 2 ^ (i - 1) ≤ j1, 0 < i, 0 ≤ j0, 0 ≤ j1 + j0 ⊦ cast(i, j1 + j0) = cast(i, i1)

Rule argument

seq: ⊦ i0 = i - j ↔ i = i0 + j subst: [i, j, i0] → [j0 + j1, 2 ^ i, i1] rotate: T spec: int-abs inst: name: elim-sub

Additional information

Used simplifier rules: ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: j0 + j1, 2 ^ i, i1