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

st[r -- i '] = refval(r0), cyclic(str, r0, st), is_array(str, r, st), i < st[r -- _length] .intval, is_reftype(st[r -- _type] .type .type), st[r0 -- _type] .type ≤ st[r -- _type] .type .type, 0 ≤ i, 0 < st[r -- _length] .intval ⊦ cyclic(str, r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ cyclic(str, r, st) ↔ (∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[r -- _type] .type, st))
Proof step 17:
st[r -- i '] = refval(r0), ∃ refs. dups(refs) ∧ refs .first = r0 ∧ validrefs(str, refs, st[r0 -- _type] .type, st), is_array(str, r, st), i < st[r -- _length] .intval, is_reftype(st[r -- _type] .type .type), st[r0 -- _type] .type ≤ st[r -- _type] .type .type, 0 ≤ i, 0 < st[r -- _length] .intval ⊦ cyclic(str, r, st)

Rule argument

[crewrite-arg: cyclic-def-simple, F, [st, r, str] → [st, r0, str]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r0, str)]]