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Proof step 57 from proof junkrefs-put-refval-02 (previous step)

junkrefs(str, r1 ' + acc, ty, st[r -- i ', refval(r0)]), mkarraytype(st[r0 -- _type] .type) ≤ st[r -- _type] .type, is_valid_ref(str, r1, st), st[r1 -- _type] .type ≤ ty, ∀ st, r0, r, str, ty, i. mkarraytype(st[r0 -- _type] .type) ≤ st[r -- _type] .type ∧ junkrefs(str, acc, ty, st[r -- i ', refval(r0)]) → r = jvmref ∨ r0 = jvmref ∨ junkrefs(str, acc, ty, st) ∨ junkref(str, r0, st) ⊦ r1 = jvmref, r0 = jvmref, r = jvmref, junkrefs(str, r1 ' + acc, ty, st), junkref(str, r0, 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 56:
junkrefs(str, r1 ' + acc, ty, st[r -- i ', refval(r0)]), mkarraytype(st[r0 -- _type] .type) ≤ st[r -- _type] .type, is_obj(str, r1, st) ∨ is_array(str, r1, st), st[r1 -- _type] .type ≤ ty, ∀ st, r0, r, str, ty, i. mkarraytype(st[r0 -- _type] .type) ≤ st[r -- _type] .type ∧ junkrefs(str, acc, ty, st[r -- i ', refval(r0)]) → r = jvmref ∨ r0 = jvmref ∨ junkrefs(str, acc, ty, st) ∨ junkref(str, r0, st) ⊦ r1 = jvmref, r0 = jvmref, r = jvmref, junkrefs(str, r1 ' + acc, ty, st), junkref(str, r0, st)

Rule argument

[speclemmaarg: ,is_valid_ref(str, r, st) ↔ is_obj(str, r, st) ∨ is_array(str, r, st) ,[st, r, str] → [st, r1, str] ,F ,addfuns , ,is-valid-ref-stronger-def ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r1, str)]]