| st[r -- mkfs(class0, ty, fieldvar) '] = refval(jvmref), st[r -- _type] .type ≤ mkclasstype(class), st[r -- _type] .type ≤ ty, ty ≤ mkclasstype(class), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), is_obj(str, r, st), is_classtype(st[r -- _type] .type), ∀ 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, cyclic(str, r, st), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref |
st[r -- mkfs(class0, ty, fieldvar) '] = refval(jvmref), st[r -- _type] .type ≤ mkclasstype(class), st[r -- _type] .type ≤ ty, ty ≤ mkclasstype(class), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), is_obj(str, r, st), is_classtype(st[r -- _type] .type), ∀ 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, cyclic(str, r, st), validrefs(str, r ' + jvmref ', st[(r ' + jvmref ') .first -- _type] .type, st) ∧ r ' + jvmref ' ≠ [] ∧ (r ' + jvmref ') .first = r ∧ (r ' + jvmref ') .last = jvmref
[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r ' + jvmref ')]]