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Proof step 21 from proof putarray-addarray-one (previous step)

r0 -- i ' ∈ addarray(r0, ty, n→i(# vals) + 1, st) ↔ r0 -- i ' ∈ addarray(r0, ty, refval(jvmref) ' + vals, st), is_reftype(ty), i ≤ 0 ∨ n→i(# vals) < i, i < 0 ∨ n→i(# vals) < i ⊦ (addarray(r0, ty, n→i(# vals) + 1, st)[r0 -- i ']) = st[r0 -- i '], ¬ i ≤ 0 ∧ ¬ n→i(# vals) < i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ i < 0 ∨ j ≤ i → (addarray(r, ty, j, st)[r -- i ']) = st[r -- i ']
Proof step 20:
⊦ r -- j ' ∈ addarray(r, ty, vals, st) ↔ r -- j ' ∈ st ∨ 0 ≤ j ∧ j < n→i(# vals)

Rule argument

[crewrite-arg: at-1dim-other-index , F , [i, st, j, ty, r] → [i, st, n→i(# vals) + 1, ty, r0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ rk ∈ st → st[rk] = ∅[rk]], [CSIMPSEQ : ⊦ ∅[rk] = noval], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (i, st, n→i(# vals) + 1, ty, r0)]]