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Proof step 85 from proof validrefs-del-junkrefs (previous step)

st[r0 -- _type] .type ≤ ty, junkrefs(str, r0 ' + (r1 ' + acc) + r ', ty, st -- r), is_valid_ref(str, r0, st), ∀ st, r0, ty, str, r. st[r0 -- _type] .type ≤ ty ∧ junkrefs(str, (r0 ' + acc) + r ', ty, st -- r) → r = r0 ∨ junkref(str, r0, st) ∨ r ∈ acc ∨ validrefs(str, r0 ' + acc + r ', ty, st) ⊦ r = r0, r = r1, r0 = jvmref, junkref(str, r0, st), r ∈ acc, validrefs(str, r0 ' + (r1 ' + acc) + r ', ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 49:
⊦ is_valid_ref(str, r, st) ↔ is_obj(str, r, st) ∨ is_array(str, r, st)
Proof step 84:
st[r0 -- _type] .type ≤ ty, junkrefs(str, r0 ' + (r1 ' + acc) + r ', ty, st -- r), is_obj(str, r0, st) ∨ is_array(str, r0, st), ∀ st, r0, ty, str, r. st[r0 -- _type] .type ≤ ty ∧ junkrefs(str, (r0 ' + acc) + r ', ty, st -- r) → r = r0 ∨ junkref(str, r0, st) ∨ r ∈ acc ∨ validrefs(str, r0 ' + acc + r ', ty, st) ⊦ r = r0, r = r1, r0 = jvmref, junkref(str, r0, st), r ∈ acc, validrefs(str, r0 ' + (r1 ' + acc) + r ', ty, st)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r0, str)]]