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Proof step 33 from proof getarray-put=set (previous step)

0 ≤ i1, i1 < j, 0 < j, ∀ val, st, i, r, i1, j0. i→n(j0) < i→n(j) → (0 < j0 ∧ i1 < j0 ∧ 0 ≤ i1 → getarray(r, i, j0, st[r -- (i1 + i) ', val]) = (getarray(r, i, j0, st)[i→n(i1), val])) ⊦ getarray(r, i, j, st[r -- (i1 + i) ', val]) = (getarray(r, i, j, st)[i→n(i1), val])

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 32:
1 < j, 0 ≤ i1, i1 < j, 0 < j, ∀ val, st, i, r, i1, j0. i→n(j0) < i→n(j) → (0 < j0 ∧ i1 < j0 ∧ 0 ≤ i1 → getarray(r, i, j0, st[r -- (i1 + i) ', val]) = (getarray(r, i, j0, st)[i→n(i1), val])) ⊦ getarray(r, i, j - 1, st[r -- (i1 + i) ', val]) + (st[r -- (i1 + i) ', val][r -- (i + j - 1) ']) = (getarray(r, i, j, st)[i→n(i1), val])

Rule argument

[crewrite-arg: getArray-rec , F , [st, j, i, r] → [st[r -- (i1 + i) ', val], j, i, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ 0 < i → (i ≤ 1 ↔ i = 1)], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ i = i + j ↔ j = 0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ 0 ≤ i → (i < 1 ↔ i = 0)], [CSIMPSEQ : ⊦ (val ')[0, val0] = val0 '], [CSIMPSEQ : ⊦ val ' = val0 ' ↔ val = val0])], [EXTRATERMS : (st[r -- (i1 + i) ', val], j, i, r)]]