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Proof step 17 from proof cyclic-put-badarrayfield (previous step)

r1 ∈ refs, validrefs(str, refs + r1 ', st[refs .first -- _type] .type, st), is_arraytype(st[r0 -- _type] .type) ⊦ fs ' = _type, fs ' = _length, cyclic(str, refs .first, st[r0 -- fs ', val]), junkref(str, refs .first, st), dups(refs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ cyclic(str, r, st) ↔ (∃ refs, r0. ¬ dups(refs) ∧ r0 ∈ refs ∧ refs .first = r ∧ validrefs(str, refs + r0 ', st[r -- _type] .type, st))
Proof step 16:
r1 ∈ refs, validrefs(str, refs + r1 ', st[refs .first -- _type] .type, st), is_arraytype(st[r0 -- _type] .type) ⊦ fs ' = _type, fs ' = _length, ∃ refs0, r1. ¬ dups(refs0) ∧ r1 ∈ refs0 ∧ refs0 .first = refs .first ∧ validrefs(str, refs0 + r1 ', (st[r0 -- fs ', val][refs .first -- _type]) .type, st[r0 -- fs ', val]), junkref(str, refs .first, st), dups(refs)

Rule argument

[crewrite-arg: cyclic-def-shortest , F , [st, r, str] → [st[r0 -- fs ', val], refs .first, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- fs ', val], refs .first, str)]]