| ∀ r, str, ty, st. r ∈ acc ∧ validrefs(str, acc, ty, st) → r = jvmref ∨ is_valid_ref(str, r, st), r ∈ r0 + acc, validrefs(str, r0 + acc, ty, st) ⊦ r = jvmref, is_valid_ref(str, r, st) |
⊦ ¬ is_valid_ref(str, r, st) → (validrefs(str, r ' + refs, ty, st) ↔ r = jvmref ∧ refs = [])
validrefs(str, r0 ' + acc, ty, st), r ∈ acc, ∀ r, str, ty, st. r ∈ acc ∧ validrefs(str, acc, ty, st) → r = jvmref ∨ is_valid_ref(str, r, st) ⊦ r = jvmref, r = r0, is_valid_ref(str, r, st)
[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]