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Proof step 4 from proof getArray-rec-01 (previous step)

0 ≤ i0 ⊦ getarray(r, i, i0 + 1, st) = getarray(r, i, i0, st) + st[r -- (i + i0) '] '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ 1 < j → getarray(r, i, j, st) = getarray(r, i, j - 1, st) + st[r -- (i + j - 1) ']
Proof step 2:
⊦ getarray(r, i, 1, st) = st[r -- i '] '
Proof step 3:
⊦ getarray(r, i, 0, st) = []

Rule argument

[crewrite-arg: getArray-rec, F, [st, j, i, r] → [st, i0 + 1, i, r]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ vals + vals0 = vals + vals1 ↔ vals0 = vals1], [CSIMPSEQ : ⊦ vals + val = vals + val '], [CSIMPSEQ : ⊦ ((* i)) + i0 - ((* j)) = (i - j) + i0], [CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ [] + vals = vals], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ val ' = val0 ' ↔ val = val0])], [EXTRATERMS : (st, i0 + 1, i, r)]]