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Proof step 70 from proof validrefs-subset-01 (previous step)

validrefs(str, r0 ' + acc, ty, st), st ⊆ st0, is_obj(str, r0, st) ∨ is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str0, ty0, st1, st2. validrefs(str0, acc, ty0, st1) ∧ st1 ⊆ st2 ∧ ¬ junkref(str0, acc .first, st1) ∧ acc ≠ [] → validrefs(str0, acc, ty0, st2) ⊦ r0 = jvmref, junkref(str, r0, st), validrefs(str, r0 ' + acc, ty, st0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ r ≠ jvmref ∧ ¬ is_valid_ref(str, r, st) → junkref(str, r, st)
Proof step 69:
¬ (r0 ≠ jvmref ∧ ¬ is_valid_ref(str, r0, st)), validrefs(str, r0 ' + acc, ty, st), st ⊆ st0, is_obj(str, r0, st) ∨ is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str0, ty0, st1, st2. validrefs(str0, acc, ty0, st1) ∧ st1 ⊆ st2 ∧ ¬ junkref(str0, acc .first, st1) ∧ acc ≠ [] → validrefs(str0, acc, ty0, st2) ⊦ r0 = jvmref, junkref(str, r0, st), validrefs(str, r0 ' + acc, ty, st0)

Rule argument

[speclemmaarg: ,r ≠ jvmref ∧ ¬ is_valid_ref(str, r, st) → junkref(str, r, st) ,[st, r, str] → [st, r0, str] ,F ,junkrefs , ,junkref-is-junk ]

Additional information

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