| st[r -- _type] .type = mkclasstype(class1), is_typevalue(st[r -- _type]), r -- _type ∈ st, class+∃(str, class1), class1 ≤ class2, r ∈ st, class1 ≤ class, class2 ≤ class, mkfs(class0, mkclasstype(class2), fieldvar) ' ∈ instfields(class), is_obj(r, class1, st), ∀ r, str, st0. # st0 .refs < # st .refs → ( ¬ junkref(str, r, st0) ∧ ¬ cyclic(str, r, st0) ∧ is_obj(str, r, st0) ∧ r ≠ jvmref ∧ (∃ fs, class. fs ' ∈ instfields(class) ∧ fs .type ≤ mkclasstype(class) ∧ st0[r -- _type] .type ≤ fs .type) → (∃ refs. validrefs(str, refs, st0[r -- _type] .type, st0) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref)) ⊦ r = jvmref, is_abstract(class1), cyclic(str, r, st), is_referencevalue(st[r -- mkfs(class0, mkclasstype(class2), fieldvar) ']), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref |
⊦ is_obj(r, class, st) ↔ r ≠ jvmref ∧ (r -- _type) × typeval(mkclasstype(class)) ∈ st ∧ goodfieldsandtypes(r, instfields(class), st)
st[r -- _type] .type = mkclasstype(class1), is_typevalue(st[r -- _type]), r -- _type ∈ st, class+∃(str, class1), class1 ≤ class2, r ∈ st, class1 ≤ class, class2 ≤ class, mkfs(class0, mkclasstype(class2), fieldvar) ' ∈ instfields(class), r ≠ jvmref ∧ (r -- _type) × typeval(mkclasstype(class1)) ∈ st ∧ goodfieldsandtypes(r, instfields(class1), st), ∀ r, str, st0. # st0 .refs < # st .refs → ( ¬ junkref(str, r, st0) ∧ ¬ cyclic(str, r, st0) ∧ is_obj(str, r, st0) ∧ r ≠ jvmref ∧ (∃ fs, class. fs ' ∈ instfields(class) ∧ fs .type ≤ mkclasstype(class) ∧ st0[r -- _type] .type ≤ fs .type) → (∃ refs. validrefs(str, refs, st0[r -- _type] .type, st0) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref)) ⊦ r = jvmref, is_abstract(class1), cyclic(str, r, st), is_referencevalue(st[r -- mkfs(class0, mkclasstype(class2), fieldvar) ']), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref
[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, class1, r)]]