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Proof step 17 from proof cast-mult-add-h (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 18:
j0 = i0 + 2 ^ i, 0 ≤ i, 0 < i, j < 0, 0 ≤ j0, j < ~1, j0 < 2 ^ i ⊦ cast(i, i0) = cast(i, j0)

Rule argument

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

Additional information

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