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Proof step 30 from proof unchanged-lookup-list-generic (previous step)

st0[r -- sk] = st[r -- sk], junkref(str, st[r -- sk] .refval, st), unchanged(str, st[r -- sk] .refval, st, st0), unchanged(str, r, st, st0), fits(st[r -- sk] .refval, sks0, st0), fits(st[r -- sk] .refval, sks0, st), is_referencevalue(st[r -- sk]), is_valid_ref(str, r, st), is_arraytype(st[r -- _type] .type) → sk = _length ∨ is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval, is_classtype(st0[r -- _type] .type) → sk ∈ instfields(st0[r -- _type] .type .class), is_arraytype(st0[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st0[r -- _length] .intval, is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval, is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class) ⊦ sks0 = [], st[st[r -- sk] .refval -- sks0] = st0[st[r -- sk] .refval -- sks0], r = jvmref, junkref(str, r, st), junkref(str, r, st0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: addfuns instance-name: lemma-name: is_valid_ref antecedent: succedent: ¬ is_obj(str, r, st) → (is_valid_ref(str, r, st) ↔ is_array(str, r, st)) substlist: [st, r, str] → [st, r, str] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 7)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r, str)]]