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Proof step 83 from proof addarray-put-01 (previous step)

0 < j, r -- i ' ∈ addarray(r, ty, mklist(initial_value(ty), i→n(j)) + val ' + mklist(initial_value(ty), i→n(i0)), st), 0 ≤ i0, 0 ≤ i0 + j, i ≤ j + i0, 0 ≤ i ⊦ j = 0, i = j, r -- i ' ∈ addarray(r, ty, i0 + j + 1, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 73:
⊦ r -- j ' ∈ addarray(r, ty, vals, st) ↔ r -- j ' ∈ st ∨ 0 ≤ j ∧ j < n→i(# vals)
Proof step 82:
0 < j, r -- i ' ∈ st ∨ 0 ≤ i ∧ i < n→i(# (mklist(initial_value(ty), i→n(j)) + val ' + mklist(initial_value(ty), i→n(i0)))), 0 ≤ i0, 0 ≤ i0 + j, i ≤ j + i0, 0 ≤ i ⊦ j = 0, i = j, r -- i ' ∈ addarray(r, ty, i0 + j + 1, st)

Rule argument

[crewrite-arg: in-add , F , [st, vals, ty, j, r] → [st, mklist(initial_value(ty), i→n(j)) + val ' + mklist(initial_value(ty), i→n(i0)), ty, i, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, mklist(initial_value(ty), i→n(j)) + val ' + mklist(initial_value(ty), i→n(i0)), ty, i, r)]]