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Proof step 16 from proof validreflist-getarray-less-02 (previous step)

0 ≤ j, 0 ≤ i, j + i ≤ st[r -- _length] .intval, validrefnotnull(str, r, mkarraytype(ty), st), is_reftype(ty), ∀ j, st, r, str, ty, i0. i→n(i0) < i→n(i) → ( is_reftype(ty) ∧ validrefnotnull(str, r, mkarraytype(ty), st) ∧ j + i0 ≤ st[r -- _length] .intval ∧ 0 ≤ i0 ∧ 0 ≤ j → r = jvmref ∨ validreflist(str, getarray(r, j, i0, st), ty, st)) ⊦ r = jvmref, validreflist(str, getarray(r, j, i, st), ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 0 < j → getarray(r, i, j, st) = st[r -- i '] ' + getarray(r, i + 1, j - 1, st)
Proof step 3:
⊦ validreflist(str, [], ty, st)
Proof step 15:
0 < i, 0 ≤ j, 0 ≤ i, j + i ≤ st[r -- _length] .intval, validrefnotnull(str, r, mkarraytype(ty), st), is_reftype(ty), ∀ j, st, r, str, ty, i0. i→n(i0) < i→n(i) → ( is_reftype(ty) ∧ validrefnotnull(str, r, mkarraytype(ty), st) ∧ j + i0 ≤ st[r -- _length] .intval ∧ 0 ≤ i0 ∧ 0 ≤ j → r = jvmref ∨ validreflist(str, getarray(r, j, i0, st), ty, st)) ⊦ r = jvmref, validreflist(str, st[r -- j '] ' + getarray(r, j + 1, i - 1, st), ty, st)

Rule argument

[speclemmaarg: , 0 < j → getarray(r, i, j, st) = st[r -- i '] ' + getarray(r, i + 1, j - 1, st) ,[st, j, i, r] → [st, i, j, r] ,F ,storearrays , ,get-rec-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ getarray(r, i, 0, st) = []])], [EXTRATERMS : (st, i, j, r)]]