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Proof step 71 from proof junkrefs-put-null-01 (previous step)

junkrefs(str, r0 ' + acc, ty, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), is_reftype(ty0), is_valid_ref(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str, ty, st, fs, r. ¬ junkrefs(str, acc, ty, st) ∧ is_reftype(fs .type) → ¬ junkrefs(str, acc, ty, st[r -- fs ', refval(jvmref)]) ⊦ r0 = 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 70:
junkrefs(str, r0 ' + acc, ty, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), is_reftype(ty0), is_obj(str, r0, st) ∨ is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str, ty, st, fs, r. ¬ junkrefs(str, acc, ty, st) ∧ is_reftype(fs .type) → ¬ junkrefs(str, acc, ty, st[r -- fs ', refval(jvmref)]) ⊦ r0 = 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)]]