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Proof step 19 from proof junkref-rec-case (previous step)

⊦ junkref(str, r, st) ↔ r ≠ jvmref ∧ ¬ is_valid_ref(str, r, st) ∨ r ≠ jvmref ∧ is_obj(str, r, st) ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- fs '] .refval ≠ jvmref ∧ (¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st[r -- fs '] .refval, st))) ∨ r ≠ jvmref ∧ is_array(str, r, st) ∧ (∃ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ st[r -- i '] .refval ≠ jvmref ∧ (¬ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∨ junkref(str, st[r -- i '] .refval, st)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ r ≠ jvmref ∧ ¬ is_valid_ref(str, r, st) → junkref(str, r, st)
Proof step 18:
¬ (r ≠ jvmref ∧ ¬ is_valid_ref(str, r, st)) ⊦ junkref(str, r, st) ↔ r ≠ jvmref ∧ ¬ is_valid_ref(str, r, st) ∨ r ≠ jvmref ∧ is_obj(str, r, st) ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- fs '] .refval ≠ jvmref ∧ (¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st[r -- fs '] .refval, st))) ∨ r ≠ jvmref ∧ is_array(str, r, st) ∧ (∃ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ st[r -- i '] .refval ≠ jvmref ∧ (¬ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∨ junkref(str, st[r -- i '] .refval, st)))

Rule argument

[crewrite-arg: junkref-is-junk, F, [st, r, str] → [st, r, str]]

Additional information

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