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Proof step 14 from proof getarray-union-03 (previous step)

r -- _length ∈ st, j + i ≤ st[r -- _length] .intval, r ∈ st, 0 ≤ i, ∀ i0. ¬ i0 < i ∧ ¬ i + j ≤ i0 → r -- i0 ' ∈ st, ∀ st0, i, st, r, j0. i→n(j0) < i→n(j) → ( true → ( r -- _length ∈ st ∧ 0 ≤ i ∧ j0 ≤ st[r -- _length] .intval - i ∧ (∀ i1. i ≤ i1 ∧ i1 < i + j0 → r -- i1 ' ∈ st) → getarray(r, i, j0, st0 ∪ st) = getarray(r, i, j0, st))) ⊦ getarray(r, i, j, st0 ∪ st) = getarray(r, i, j, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ 0 < j → getarray(r, i, j, st) = st[r -- i '] ' + getarray(r, i + 1, j - 1, st)
Proof step 2:
⊦ j ≤ 0 → getarray(r, i, j, st) = []
Proof step 13:
0 < j, r -- _length ∈ st, j + i ≤ st[r -- _length] .intval, r ∈ st, 0 ≤ i, ∀ i0. ¬ i0 < i ∧ ¬ i + j ≤ i0 → r -- i0 ' ∈ st, ∀ st0, i, st, r, j0. i→n(j0) < i→n(j) → ( true → ( r -- _length ∈ st ∧ 0 ≤ i ∧ j0 ≤ st[r -- _length] .intval - i ∧ (∀ i1. i ≤ i1 ∧ i1 < i + j0 → r -- i1 ' ∈ st) → getarray(r, i, j0, st0 ∪ st) = getarray(r, i, j0, st))) ⊦ (st0 ∪ st)[r -- i '] ' + getarray(r, i + 1, j - 1, st0 ∪ st) = getarray(r, i, j, st)

Rule argument

[crewrite-arg: get-rec-01, F, [st, j, i, r] → [st0 ∪ st, j, i, r]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (st0 ∪ st, j, i, r)]]