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Proof step 23 from proof cast-law-add-pos (previous step)

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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ i + j = j + i
Proof step 25:
j1 + j0 = 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: ⊦ i + j = j + i subst: [j, i] → [j1, j0] rotate: F spec: int-basic2 inst: name: add-c

Additional information

Used simplifier rules: ⊦ i + j = j + i; Used terms: j1, j0