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Proof step 18 from proof cyclic-addobj (previous step)

fis[mkfs(class0, ty, fieldvar) '] = refval(r1), fis .keys = instfields(class), st[r1 -- _type] = typeval(ty0), validrefs(str, r1 ' + refs, ty, addobj(r, class, fis, st)), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), newref(r, st), is_obj(str, r, addobj(r, class, fis, st)), mkfs(class0, ty, fieldvar) ' ∈ fis, okval(refval(r1), ty), r1 -- _type ∈ st, ty0 ≤ ty, r1 ∈ st, validrefs(str, r1 ' + refs, ty, st), ∀ fs, r0. fs ' × refval(r0) ∈ fis → ¬ junkref(str, r0, st) ∧ ¬ cyclic(str, r0, st) ⊦ r1 = jvmref, r = jvmref, r ∈ refs, junkref(str, r1, st), cyclic(str, r1, st), ¬ dups(refs) ∧ ¬ r1 ∈ refs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ cyclic(str, r, st) ↔ (∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[r -- _type] .type, st))
Proof step 17:
fis[mkfs(class0, ty, fieldvar) '] = refval(r1), fis .keys = instfields(class), st[r1 -- _type] = typeval(ty0), validrefs(str, r1 ' + refs, ty, addobj(r, class, fis, st)), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), newref(r, st), is_obj(str, r, addobj(r, class, fis, st)), mkfs(class0, ty, fieldvar) ' ∈ fis, okval(refval(r1), ty), r1 -- _type ∈ st, ty0 ≤ ty, r1 ∈ st, validrefs(str, r1 ' + refs, ty, st), ∀ fs, r0. fs ' × refval(r0) ∈ fis → ¬ junkref(str, r0, st) ∧ ¬ cyclic(str, r0, st) ⊦ r1 = jvmref, r = jvmref, r ∈ refs, junkref(str, r1, st), ∃ refs. dups(refs) ∧ refs .first = r1 ∧ validrefs(str, refs, st[r1 -- _type] .type, st), ¬ dups(refs) ∧ ¬ r1 ∈ refs

Rule argument

[crewrite-arg: cyclic-def-simple, F, [st, r, str] → [st, r1, str]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r1, str)]]