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Proof step 12 from proof cyclic-addarray-this-01 (previous step)

vals[i→n(i)] = refval(r1), refval(r1) ∈ vals, validrefs(str, r1 ' + refs, ty, addarray(r0, ty, vals, st)), 0 ≤ i, is_array(str, r0, addarray(r0, ty, vals, st)), newref(r0, st), i < n→i(# vals), validrefs(str, r1 ' + refs, ty, st), ∀ r. refval(r) ∈ vals → ¬ junkref(str, r, st) ∧ ¬ cyclic(str, r, st) ⊦ vals = [], r0 = jvmref, r0 = r1, r0 ∈ refs, cyclic(str, r1, st), junkref(str, r1, st), ¬ dups(refs) ∧ ¬ r1 ∈ refs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ cyclic(str, r, st) ↔ (∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[r -- _type] .type, st))
Proof step 11:
vals[i→n(i)] = refval(r1), refval(r1) ∈ vals, validrefs(str, r1 ' + refs, ty, addarray(r0, ty, vals, st)), 0 ≤ i, is_array(str, r0, addarray(r0, ty, vals, st)), newref(r0, st), i < n→i(# vals), validrefs(str, r1 ' + refs, ty, st), ∀ r. refval(r) ∈ vals → ¬ junkref(str, r, st) ∧ ¬ cyclic(str, r, st) ⊦ vals = [], r0 = jvmref, r0 = r1, r0 ∈ refs, ∃ refs. dups(refs) ∧ refs .first = r1 ∧ validrefs(str, refs, st[r1 -- _type] .type, st), junkref(str, r1, 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)]]