| is_arraytype(st[r0 -- _type] .type), is_array(str, r, st), st[r -- _type] .type ≤ ty, ∀ st, r0, str, ty, fs, val. is_arraytype(st[r0 -- _type] .type) ∧ validrefs(str, acc, ty, st[r0 -- fs ', val]) → fs ' = _type ∨ fs ' = _length ∨ acc = [] ∨ validrefs(str, acc, ty, st) ∨ junkref(str, acc .first, st) ∨ dups(acc .butlast), acc = [] ∨ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ acc .first = st[r -- i '] .refval ∧ validrefs(str, acc, st[r -- _type] .type .type, st[r0 -- fs ', val]) ⊦ fs ' = _type, fs ' = _length, r = jvmref, validrefs(str, r ' + acc, ty, st), junkref(str, r, st), dups((r ' + acc) .butlast), is_classtype(st[r -- _type] .type) |
⊦ is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(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 ∧ validrefs(str, refs, st[r -- _type] .type .type, st)))
is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty, is_arraytype(st[r0 -- _type] .type), is_array(str, r, st), st[r -- _type] .type ≤ ty, ∀ st, r0, str, ty, fs, val. is_arraytype(st[r0 -- _type] .type) ∧ validrefs(str, acc, ty, st[r0 -- fs ', val]) → fs ' = _type ∨ fs ' = _length ∨ acc = [] ∨ validrefs(str, acc, ty, st) ∨ junkref(str, acc .first, st) ∨ dups(acc .butlast), acc = [] ∨ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ acc .first = st[r -- i '] .refval ∧ validrefs(str, acc, st[r -- _type] .type .type, st[r0 -- fs ', val]) ⊦ fs ' = _type, fs ' = _length, r = jvmref, acc = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ acc .first = st[r -- i '] .refval ∧ validrefs(str, acc, st[r -- _type] .type .type, st)), junkref(str, r, st), dups((r ' + acc) .butlast), is_classtype(st[r -- _type] .type)
[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, acc, r, str)]]