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Proof step 64 from proof junkrefs-put-nopathex (previous step)

junkrefs(str, r1 ' + acc, ty, st[r0 -- sk, val]), is_valid_ref(str, r1, st), st[r1 -- _type] .type ≤ ty, ∀ str0, r2, st0, ty0, sk0, val0. ¬ path∃(str0, acc .first, r2, st0) ∧ ¬ junkrefs(str0, acc, ty0, st0) ∧ sk0 ≠ _type ∧ acc ≠ [] → ¬ junkrefs(str0, acc, ty0, st0[r2 -- sk0, val0]) ⊦ sk = _type, r1 = jvmref, junkrefs(str, r1 ' + acc, ty, st), path∃(str, r1, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ is_valid_ref(str, r, st) ↔ is_obj(str, r, st) ∨ is_array(str, r, st)
Proof step 63:
junkrefs(str, r1 ' + acc, ty, st[r0 -- sk, val]), is_obj(str, r1, st) ∨ is_array(str, r1, st), st[r1 -- _type] .type ≤ ty, ∀ str0, r2, st0, ty0, sk0, val0. ¬ path∃(str0, acc .first, r2, st0) ∧ ¬ junkrefs(str0, acc, ty0, st0) ∧ sk0 ≠ _type ∧ acc ≠ [] → ¬ junkrefs(str0, acc, ty0, st0[r2 -- sk0, val0]) ⊦ sk = _type, r1 = jvmref, junkrefs(str, r1 ' + acc, ty, st), path∃(str, r1, 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)]]