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Proof step 17 from proof putarray-addarray-one (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ 0 ≤ j ∧ j < i → (addarray(r, ty, i, st)[r -- j ']) = initial_value(ty)

Rule argument

[crewrite-arg: at-1dim , F , [j, st, i, ty, r] → [0, st, n→i(# vals) + 1, ty, r0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refval(r) = refval(r0) ↔ r = r0], [CSIMPSEQ : ⊦ is_reftype(ty) → initial_value(ty) = refval(jvmref)], [CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0], [CSIMPSEQ : ⊦ (~1) < i ↔ 0 ≤ i], [CSIMPSEQ : ⊦ 0 ≤ n→i(n)], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (0, st, n→i(# vals) + 1, ty, r0)]]