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Proof step 16 from proof disjoint-forward-array (previous step)

st[r1 -- i '] = refval(r3), path∃(str, r3, r0, st), path∃(str, r2, r0, st), r ∈ refs, r1 ∈ refs, i < st[r1 -- _length] .intval, is_arraytype(st[r1 -- _type] .type), 0 ≤ i, 0 < st[r1 -- _length] .intval, r2 ∈ refs, ∀ r4, r5, r6. ¬ r4 ∈ refs ∨ ¬ r5 ∈ refs ∨ r4 = r5 ∨ r6 = jvmref ∨ ¬ path∃(str, r4, r6, st) ∨ ¬ path∃(str, r5, r6, st) ⊦ r1 = jvmref, r = r1, r0 = jvmref, r3 = r2, r2 = r1, junkref(str, r1, st), r3 ∈ refs, r3 ∈ refs -l r1, path∃(str, r1, 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, r1, str] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 8)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r0, r1, str)]]