| ∀ str, ty, r, ty0, vals, st. validrefs(str, acc, ty, addarray(r, ty0, vals, st)) ∧ newref(r, st) → r = jvmref ∨ r ∈ acc ∨ validrefs(str, acc, ty, st), validrefs(str, r0 + acc, ty, addarray(r, ty0, vals, st)), newref(r, st) ⊦ r = jvmref, r ∈ r0 + acc, validrefs(str, r0 + acc, ty, st) |
newref(r, st), validrefs(str, r0 ' + acc, ty, addarray(r, ty0, vals, st)), ∀ str, ty, r, ty0, vals, st. validrefs(str, acc, ty, addarray(r, ty0, vals, st)) ∧ newref(r, st) → r = jvmref ∨ r ∈ acc ∨ validrefs(str, acc, ty, st) ⊦ r = jvmref, r = r0, r ∈ acc, validrefs(str, r0 ' + acc, ty, st)
[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]