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Proof step 23 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 ⊦ (addarray(r0, ty, n→i(# vals) + 1, st)[r0 -- i ']) = (addarray(r0, ty, refval(jvmref) ' + vals, st)[r0 -- i ']), ¬ i ≤ 0 ∧ ¬ n→i(# vals) < i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ i < 0 ∨ n→i(# vals) ≤ i → (addarray(r, ty, vals, st)[r -- i ']) = st[r -- i ']
Proof step 18:
¬ (i < 0 ∨ n→i(# (refval(jvmref) ' + vals)) ≤ i), 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 ⊦ (addarray(r0, ty, n→i(# vals) + 1, st)[r0 -- i ']) = (addarray(r0, ty, refval(jvmref) ' + vals, st)[r0 -- i ']), ¬ i ≤ 0 ∧ ¬ n→i(# vals) < i
Proof step 22:
i < 0 ∨ n→i(# (refval(jvmref) ' + vals)) ≤ i, 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 ⊦ (addarray(r0, ty, n→i(# vals) + 1, st)[r0 -- i ']) = st[r0 -- i '], ¬ i ≤ 0 ∧ ¬ n→i(# vals) < i

Rule argument

[crewrite-arg: add-at-other-index , F , [i, st, vals, ty, r] → [i, st, refval(jvmref) ' + vals, ty, r0] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i, st, refval(jvmref) ' + vals, ty, r0)]]