| st[r0 -- _type] .type = mkclasstype(class), st[r -- _type] .type ≤ ty, validrefs(str, r ' + r1 ' + refs, ty, st[r0 -- fs ', val]), ∀ str0, ty0, st0, fs0, r2, val0. ¬ validrefs(str0, r1 ' + refs, ty0, st0) ∧ ¬ junkref(str0, r1, st0) ∧ fs0 ' ≠ _type ∧ is_classtype(st0[r2 -- _type] .type) ∧ ¬ fs0 ' ∈ instfields(st0[r2 -- _type] .type .class) → ¬ validrefs(str0, r1 ' + refs, ty0, st0[r2 -- fs0 ', val0]), is_obj(str, r, st[r0 -- fs ', val]) ∨ is_array(str, r, st[r0 -- fs ', val]) ⊦ r = jvmref, fs ' = _type, validrefs(str, r ' + r1 ' + refs, ty, st), junkref(str, r, st), fs ' ∈ instfields(class), r ∈ (r1 ' + refs) .butlast, dups((r1 ' + refs) .butlast) |
⊦ r ≠ jvmref ∧ ¬ is_valid_ref(str, r, st) → junkref(str, r, st)
¬ (r ≠ jvmref ∧ ¬ is_valid_ref(str, r, st)), st[r0 -- _type] .type = mkclasstype(class), st[r -- _type] .type ≤ ty, validrefs(str, r ' + r1 ' + refs, ty, st[r0 -- fs ', val]), ∀ str0, ty0, st0, fs0, r2, val0. ¬ validrefs(str0, r1 ' + refs, ty0, st0) ∧ ¬ junkref(str0, r1, st0) ∧ fs0 ' ≠ _type ∧ is_classtype(st0[r2 -- _type] .type) ∧ ¬ fs0 ' ∈ instfields(st0[r2 -- _type] .type .class) → ¬ validrefs(str0, r1 ' + refs, ty0, st0[r2 -- fs0 ', val0]), is_obj(str, r, st[r0 -- fs ', val]) ∨ is_array(str, r, st[r0 -- fs ', val]) ⊦ r = jvmref, fs ' = _type, validrefs(str, r ' + r1 ' + refs, ty, st), junkref(str, r, st), fs ' ∈ instfields(class), r ∈ (r1 ' + refs) .butlast, dups((r1 ' + refs) .butlast)
[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r, str)]]