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Proof step 8 from proof validrefs-put-notin-03 (previous step)

st[r -- _type] .type ≤ ty, is_valid_ref(r, st), is_obj(str, r, st), is_array(str, r, st[r -- sk, val]) ⊦ sk = _length, sk = _type, r0 = st[r -- sk] .refval, val .refval = r0, r = r0, r = jvmref, validrefs(str, r ' + r0 ' + refs1, ty, st[r -- sk, val]) ↔ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ r0 = st[r -- fs '] .refval ∧ validrefs(str, st[r -- fs '] .refval ' + refs1, fs .type, st)), r0 ∈ refs1, dups(refs1), r ∈ refs1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: okfuns instance-name: lemma-name: is_array-arraytype antecedent: succedent: ¬ is_arraytype(st[r -- _type] .type) → ¬ is_array(str, r, st) substlist: [st, r, str] → [st[r -- sk, val], r, str] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 3)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javastore, , at-other-16, ⊦ sk ≠ sk0 → (st[r -- sk, val] [r0 -- sk0 ] ) = st[r0 -- sk0]], [CSIMPNAMEDSEQ : addfuns, , is_obj-arraytype, ⊦ is_arraytype (st[r -- _type] .type) → ¬ is_obj(str, r, st)])], [EXTRATERMS : (st[r -- sk, val], r, str)]]