| acc .first = (st[r0 -- fs ', val][r -- fs0 ']) .refval, is_obj(str, r, st), is_arraytype(st[r0 -- _type] .type), is_obj(str, r, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, fs0 ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r0 -- fs ', val][r -- fs0 ']), validrefs(str, acc, fs0 .type, st[r0 -- fs ', val]), ∀ st0, r1, str0, ty0, fs1, val0. is_arraytype(st0[r1 -- _type] .type) ∧ validrefs(str0, acc, ty0, st0[r1 -- fs1 ', val0]) → fs1 ' = _type ∨ fs1 ' = _length ∨ validrefs(str0, acc, ty0, st0) ∨ junkref(str0, acc .first, st0) ⊦ fs ' = _type, fs ' = _length, r = jvmref, acc = [], is_arraytype(st[r -- _type] .type), junkref(str, r, st), dups(acc .butlast), r ∈ acc .butlast, ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ acc .first = st[r -- fs '] .refval ∧ validrefs(str, acc, fs .type, st) |
acc .first = (st[r0 -- fs ', val][r -- fs0 ']) .refval, is_obj(str, r, st), is_arraytype(st[r0 -- _type] .type), is_obj(str, r, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, fs0 ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r0 -- fs ', val][r -- fs0 ']), validrefs(str, acc, fs0 .type, st[r0 -- fs ', val]), ∀ st0, r1, str0, ty0, fs1, val0. is_arraytype(st0[r1 -- _type] .type) ∧ validrefs(str0, acc, ty0, st0[r1 -- fs1 ', val0]) → fs1 ' = _type ∨ fs1 ' = _length ∨ validrefs(str0, acc, ty0, st0) ∨ junkref(str0, acc .first, st0) ⊦ fs ' = _type, fs ' = _length, r = jvmref, acc = [], is_arraytype(st[r -- _type] .type), junkref(str, r, st), dups(acc .butlast), r ∈ acc .butlast, fs0 ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs0 ']) ∧ acc .first = st[r -- fs0 '] .refval ∧ validrefs(str, acc, fs0 .type, st)
[[CONCRETESIMPRULES : ()], [EXTRATERMS : (fs0)]]