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Proof step 14 from proof getarray-put=set (previous step)

0 ≤ i1, 0 < i1, ∀ val, st, i, r, i2, j0. i→n(j0) < i→n(i1 + 1) → (0 < j0 ∧ i2 < j0 ∧ 0 ≤ i2 → getarray(r, i, j0, st[r -- (i2 + i) ', val]) = (getarray(r, i, j0, st)[i→n(i2), val])) ⊦ getarray(r, i, i1, st[r -- (i1 + i) ', val]) + val ' = (getarray(r, i, i1 + 1, st)[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 4:
⊦ getarray(r, i, 0, st) = []
Proof step 5:
⊦ getarray(r, i, 1, st) = st[r -- i '] '
Proof step 13:
1 < i1 + 1, 0 ≤ i1, 0 < i1, ∀ val, st, i, r, i2, j0. i→n(j0) < i→n(i1 + 1) → (0 < j0 ∧ i2 < j0 ∧ 0 ≤ i2 → getarray(r, i, j0, st[r -- (i2 + i) ', val]) = (getarray(r, i, j0, st)[i→n(i2), val])) ⊦ getarray(r, i, i1, st[r -- (i1 + i) ', val]) + val ' = (getarray(r, i, i1 + 1 - 1, st) + st[r -- (i + i1 + 1 - 1) '])[i→n(i1), val]

Rule argument

[crewrite-arg: getArray-rec, F, [st, j, i, r] → [st, i1 + 1, i, r]]

Additional information

[[CONCRETESIMPRULES : ([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], [CSIMPFORWARD : ⊦ i < i0 ∧ i = i1 → i1 < i0], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ [] + vals = vals], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ (val ')[0, val0] = val0 '], [CSIMPSEQ : ⊦ val ' = val0 ' ↔ val = val0])], [EXTRATERMS : (st, i1 + 1, i, r)]]