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Proof step 43 from proof junkrefs-put-null-02 (previous step)

junkrefs(str, r0 ' + acc, ty, st[r -- i ', refval(jvmref)]), is_reftype(st[r -- _type] .type .type), is_valid_ref(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ st, r, str, ty, i. is_reftype(st[r -- _type] .type .type) ∧ junkrefs(str, acc, ty, st[r -- i ', refval(jvmref)]) → r = jvmref ∨ junkrefs(str, acc, ty, st) ⊦ r0 = jvmref, r = jvmref, junkrefs(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 42:
junkrefs(str, r0 ' + acc, ty, st[r -- i ', refval(jvmref)]), is_reftype(st[r -- _type] .type .type), is_obj(str, r0, st) ∨ is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ st, r, str, ty, i. is_reftype(st[r -- _type] .type .type) ∧ junkrefs(str, acc, ty, st[r -- i ', refval(jvmref)]) → r = jvmref ∨ junkrefs(str, acc, ty, st) ⊦ r0 = jvmref, r = jvmref, junkrefs(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] → [st, r0, str] ,F ,addfuns , ,is-valid-ref-stronger-def ]

Additional information

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