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Proof step 13 from proof getarray-addarray-03 (previous step)

0 ≤ i1, ∀ st, val, r, i0. i→n(i0) < i→n(i1 + 1) → (0 ≤ i0 → getarray(r, 0, i0, addarray(r, val, i0, st)) = mklist(val, i→n(i0))) ⊦ getarray(r, 0, i1 + 1, addarray(r, val, i1, st)[r -- i1 ', val]) = mklist(val, i→n(i1)) + val '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 1 < j → getarray(r, i, j, st) = getarray(r, i, j - 1, st) + st[r -- (i + j - 1) ']
Proof step 7:
¬ 1 < i1 + 1, 0 ≤ i1, ∀ st, val, r, i0. i→n(i0) < i→n(i1 + 1) → (0 ≤ i0 → getarray(r, 0, i0, addarray(r, val, i0, st)) = mklist(val, i→n(i0))) ⊦ getarray(r, 0, i1 + 1, addarray(r, val, i1, st)[r -- i1 ', val]) = mklist(val, i→n(i1)) + val '
Proof step 12:
1 < i1 + 1, 0 ≤ i1, ∀ st, val, r, i0. i→n(i0) < i→n(i1 + 1) → (0 ≤ i0 → getarray(r, 0, i0, addarray(r, val, i0, st)) = mklist(val, i→n(i0))) ⊦ getarray(r, 0, i1 + 1 - 1, addarray(r, val, i1, st)[r -- i1 ', val]) + (addarray(r, val, i1, st)[r -- i1 ', val][r -- (0 + i1 + 1 - 1) ']) = mklist(val, i→n(i1)) + val '

Rule argument

[speclemmaarg: , 1 < j → getarray(r, i, j, st) = getarray(r, i, j - 1, st) + st[r -- (i + j - 1) '] ,[st, j, i, r] → [addarray(r, val, i1, st)[r -- i1 ', val], i1 + 1, 0, r] ,F ,storearrays , ,getArray-rec ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addarray(r, val, i1, st)[r -- i1 ', val], i1 + 1, 0, r)]]