| st[r -- i '] = refval(r1), is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, junkrefs(str, r1 ' + acc, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_valid_ref(str, r0, st), validFields(r0, fis, st), st[r1 -- _type] .type ≤ st[r -- _type] .type .type, ∀ r0, fis, st, str, r. validFields(r0, fis, st) ∧ is_valid_ref(str, r0, st) ∧ junkrefs(str, r ' + acc, st[r -- _type] .type, st) → junkref(str, r, update(r0, fis, st)) ∨ path∃(str, r, r0, st) ∨ _type ∈ fis ⊦ r = jvmref, r = r0, r1 = jvmref, _type ∈ fis, path∃(str, r, r0, st), junkref(str, r1, update(r0, fis, st)) |
⊦ 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)))
is_array(str, r, st) ∧ r ≠ r0, st[r -- i '] = refval(r1), is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, junkrefs(str, r1 ' + acc, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_valid_ref(str, r0, st), validFields(r0, fis, st), st[r1 -- _type] .type ≤ st[r -- _type] .type .type, ∀ r0, fis, st, str, r. validFields(r0, fis, st) ∧ is_valid_ref(str, r0, st) ∧ junkrefs(str, r ' + acc, st[r -- _type] .type, st) → junkref(str, r, update(r0, fis, st)) ∨ path∃(str, r, r0, st) ∨ _type ∈ fis ⊦ r = jvmref, r = r0, r1 = jvmref, _type ∈ fis, ∃ 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), junkref(str, r1, update(r0, fis, st))
[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r0, r, str)]]