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Proof step 9 from proof validrefs-del-junkrefs (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ validrefs(str, r ', ty, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st) ∧ st[r -- _type] .type ≤ ty

Rule argument

[crewrite-arg: validrefs-one, F, [st, ty, r, str] → [st, ty0, r, str]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_valid_ref(str, r, st) ∧ r ≠ jvmref → junkref(str, r, st)])], [EXTRATERMS : (st, ty0, r, str)]]