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Proof step 3 from proof putarray-addarray-one (previous step)

r0 -- sk ∈ addarray(r, ty, n→i(# vals) + 1, st) ∨ r0 = r ∧ ¬ is_fskey(sk) ∧ ¬ sk .index ≤ 0 ∧ ¬ n→i(# vals) < sk .index ↔ r0 -- sk ∈ addarray(r, ty, refval(jvmref) ' + vals, st), is_reftype(ty) ⊦ r0 -- sk ∈ addarray(r, ty, n→i(# vals) + 1, st) ∨ r0 = r ∧ is_indexkey(sk) ∧ 0 < sk .index ∧ sk .index ≤ n→i(# vals) ↔ r0 -- sk ∈ addarray(r, ty, refval(jvmref) ' + vals, st)

User applied rule case distinction

And closed the goal!

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i])]]