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Proof step 34 from proof validrefs-addarray (previous step)

newref(r, st), validrefs(str, r0 ' + acc, ty, addarray(r, ty0, vals, st)), is_valid_ref(str, r0, addarray(r, ty0, vals, st)), st[r0 -- _type] .type ≤ ty, ∀ 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, r0 = jvmref, r ∈ acc, validrefs(str, r0 ' + acc, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ is_valid_ref(str, r, st) ↔ is_obj(str, r, st) ∨ is_array(str, r, st)
Proof step 33:
newref(r, st), validrefs(str, r0 ' + acc, ty, addarray(r, ty0, vals, st)), is_obj(str, r0, addarray(r, ty0, vals, st)) ∨ is_array(str, r0, addarray(r, ty0, vals, st)), st[r0 -- _type] .type ≤ ty, ∀ 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, r0 = jvmref, r ∈ acc, validrefs(str, r0 ' + acc, ty, st)

Rule argument

[speclemmaarg: ,is_valid_ref(str, r, st) ↔ is_obj(str, r, st) ∨ is_array(str, r, st) ,[st, r, str] → [addarray(r, ty0, vals, st), r0, str] ,F ,addfuns , ,is-valid-ref-stronger-def ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addarray(r, ty0, vals, st), r0, str)]]