| ¬ (r0 ≠ jvmref ∧ (¬ is_valid_ref(str, r0, addobj(r, class, fis, st)) ∨ ¬ (addobj(r, class, fis, st)[r0 -- _type]) .type ≤ ty)), validrefs(str, r0 ' + acc, ty, addobj(r, class, fis, st)), ∀ str, ty, r, class, fis, st. validrefs(str, acc, ty, addobj(r, class, fis, st)) → validrefs(str, acc, ty, st) ∨ r ∈ acc ⊦ r0 = jvmref, r = r0, r ∈ acc, validrefs(str, r0 ' + acc, ty, st) |
validrefs(str, r0 ' + acc, ty, addobj(r, class, fis, st)), is_valid_ref(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str, ty, r, class, fis, st. validrefs(str, acc, ty, addobj(r, class, fis, st)) → validrefs(str, acc, ty, st) ∨ r ∈ acc ⊦ r0 = jvmref, r = r0, r ∈ acc, validrefs(str, r0 ' + acc, ty, st)
[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → (addobj(r, class1, fis, st) [r0 -- sk ] ) = st[r0 -- sk]], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_valid_ref (str, r, addobj(r0, class, fis, st)) ↔ is_valid_ref(str, r, st))], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]