| st1 .refs ∩ st .refs = ∅, is_array(str, r, st1), junkrefs(str, r ' + r0 ' + acc, ty, st1 ∪ st), r ∈ st1, st1[r -- _type] .type ≤ ty, ∀ st1, st, r, str, ty. st1 .refs ∩ st .refs = ∅ ∧ r ∈ st1 ∧ junkrefs(str, r ' + acc, ty, st1 ∪ st) → junkrefs(str, r ' + acc, ty, st1) ⊦ r = jvmref, ∃ i. ¬ i < 0 ∧ ¬ st1[r -- _length] .intval ≤ i ∧ is_referencevalue(st1[r -- i ']) ∧ r0 = st1[r -- i '] .refval ∧ junkrefs(str, st1[r -- i '] .refval ' + acc, st1[r -- _type] .type .type, st1) |
⊦ is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( junkrefs(str, r ' + refs, ty, st) ↔ refs ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs .first = st[r -- i '] .refval ∧ junkrefs(str, refs, st[r -- _type] .type .type, st)))
¬ (is_array(str, r, st1 ∪ st) ∧ (st1 ∪ st)[r -- _type] .type ≤ ty), st1 .refs ∩ st .refs = ∅, is_array(str, r, st1), junkrefs(str, r ' + r0 ' + acc, ty, st1 ∪ st), r ∈ st1, st1[r -- _type] .type ≤ ty, ∀ st1, st, r, str, ty. st1 .refs ∩ st .refs = ∅ ∧ r ∈ st1 ∧ junkrefs(str, r ' + acc, ty, st1 ∪ st) → junkrefs(str, r ' + acc, ty, st1) ⊦ r = jvmref, ∃ i. ¬ i < 0 ∧ ¬ st1[r -- _length] .intval ≤ i ∧ is_referencevalue(st1[r -- i ']) ∧ r0 = st1[r -- i '] .refval ∧ junkrefs(str, st1[r -- i '] .refval ' + acc, st1[r -- _type] .type .type, st1)
is_array(str, r, st1 ∪ st) ∧ (st1 ∪ st)[r -- _type] .type ≤ ty, st1 .refs ∩ st .refs = ∅, is_array(str, r, st1), r0 ' + acc ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < (st1 ∪ st)[r -- _length] .intval ∧ is_referencevalue((st1 ∪ st)[r -- i ']) ∧ (r0 ' + acc) .first = (st1 ∪ st)[r -- i '] .refval ∧ junkrefs(str, r0 ' + acc, (st1 ∪ st)[r -- _type] .type .type, st1 ∪ st)), r ∈ st1, st1[r -- _type] .type ≤ ty, ∀ st1, st, r, str, ty. st1 .refs ∩ st .refs = ∅ ∧ r ∈ st1 ∧ junkrefs(str, r ' + acc, ty, st1 ∪ st) → junkrefs(str, r ' + acc, ty, st1) ⊦ r = jvmref, ∃ i. ¬ i < 0 ∧ ¬ st1[r -- _length] .intval ≤ i ∧ is_referencevalue(st1[r -- i ']) ∧ r0 = st1[r -- i '] .refval ∧ junkrefs(str, st1[r -- i '] .refval ' + acc, st1[r -- _type] .type .type, st1)
[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st1 ∪ st, ty, r0 ' + acc, r, str)]]