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Proof step 4 from proof cyclic-one (previous step)

st[r -- mkfs(class, ty, fieldvar) '] = refval(r), is_obj(str, r, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st[r -- _type] .type ≤ ty ⊦ validrefs(str, r ', ty, st), ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[refs .first -- _type] .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 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, ty, r, str]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_obj(str, r, st) → is_valid_ref(str, r, st)])], [EXTRATERMS : (st, ty, r, str)]]