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Proof step 6 from proof unchanged-array-forward (previous step)

st[r -- i '] = refval(r0), is_valid_ref(str, r0, st), st[r0 -- _type] .type ≤ st[r -- _type] .type .type, 0 < st[r -- _length] .intval, 0 ≤ i, is_array(str, r, st), i < st[r -- _length] .intval, unchanged(str, r, st, st1) ⊦ r0 = jvmref, r = jvmref, unchanged(str, r0, st, st1), path∃(str, r, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: cyclic instance-name: lemma-name: pathex-array antecedent: succedent: is_array(str, r, st) ∧ r ≠ r0 → ( path∃(str, r, r0, st) ↔ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ ( st[r -- i '] .refval ≠ jvmref ∧ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∧ path∃(str, st[r -- i '] .refval, r0, st) ∨ st[r -- i '] .refval = jvmref ∧ r0 = jvmref))) substlist: [st, r0, r, str] → [st, r0, r, str] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 3)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r0, r, str)]]