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Proof step 13 from proof validrefs-del-junkrefs (previous step)

st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, junkrefs(str, r ', ty0, st -- r) ⊦ r = r0, r0 = jvmref, junkref(str, r0, st), validrefs(str, r ', ty0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ is_obj(str, r, st) → ( junkref(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))))
Proof step 12:
is_obj(str, r0, st), st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, junkrefs(str, r ', ty0, st -- r) ⊦ r = r0, r0 = jvmref, ∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ st[r0 -- fs '] .refval ≠ jvmref ∧ (¬ st[st[r0 -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st[r0 -- fs '] .refval, st)), validrefs(str, r ', ty0, st)

Rule argument

[speclemmaarg: , is_obj(str, r, st) → ( junkref(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)))) ,[st, r, str] → [st, r0, str] ,F ,junkrefs , ,junkref-class ]

Additional information

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