| is_valid_ref(str, r, st), is_valid_ref(str0, r, st1), st1[r -- _type] .type ≤ ty, is_valid_ref(str, r, st1), junkrefs(str, r ' + refs0, ty, st), unchanged(str0, r, st, st1), level⊆(str, str0), is_valid_ref(str0, r, st), unchangedNorec(r, st, st1), ∀ str0, st, st1, str, ty. unchanged(str0, refs0 .first, st, st1) ∧ junkrefs(str, refs0, ty, st) ∧ level⊆(str, str0) → junkrefs(str, refs0, ty, st1), ∀ r0. (path∃(str0, r, r0, st) ↔ path∃(str0, r, r0, st1)) ∧ (path∃(str0, r, r0, st) → unchangedNorec(r0, st, st1)) ⊦ r = jvmref, junkrefs(str, r ' + refs0, ty, st1) |
⊦ is_valid_ref(str, r, st) ↔ is_obj(str, r, st) ∨ is_array(str, r, st)
is_valid_ref(str, r, st), is_valid_ref(str0, r, st1), st1[r -- _type] .type ≤ ty, is_obj(str, r, st1) ∨ is_array(str, r, st1), junkrefs(str, r ' + refs0, ty, st), unchanged(str0, r, st, st1), level⊆(str, str0), is_valid_ref(str0, r, st), unchangedNorec(r, st, st1), ∀ str0, st, st1, str, ty. unchanged(str0, refs0 .first, st, st1) ∧ junkrefs(str, refs0, ty, st) ∧ level⊆(str, str0) → junkrefs(str, refs0, ty, st1), ∀ r0. (path∃(str0, r, r0, st) ↔ path∃(str0, r, r0, st1)) ∧ (path∃(str0, r, r0, st) → unchangedNorec(r0, st, st1)) ⊦ r = jvmref, junkrefs(str, r ' + refs0, ty, st1)
[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st1, r, str)]]