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Proof step 55 from proof maxpath-array (previous step)

st[r -- i '] = refval(r0), 0 < st[r -- _length] .intval, validrefs(str, r ' + refs0, st[r -- _type] .type, st), 0 ≤ i, i < st[r -- _length] .intval, is_array(str, r, st) ⊦ r ' + refs0 ∈ validrefset(str, r, st), r ∈ refs0, dups(refs0), has_reffield((r ' + refs0) .last, st), junkref(str, r, st), cyclic(str, r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 54:
⊦ is_valid_ref(str, r, st) → ( refs ∈ validrefset(str, r, st) ↔ refs ≠ [] ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st) ∧ ¬ dups(refs) ∧ validrefs(str, refs, st[r -- _type] .type, st))

Rule argument

[crewrite-arg: validrefset-def , F , [st, r, str, refs] → [st, r, str, r ' + refs0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_valid_ref(str, r, st) → ( validrefs (str, r ' + refs, ty, st) ↔ r = jvmref ∧ refs = [])], [CSIMPSEQ : ⊦ is_array(str, r, st) → is_valid_ref(str, r, st)], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ ¬ r ∈ refs → (dups(r ' + refs) ↔ dups(refs))])], [EXTRATERMS : (st, r, str, r ' + refs0)]]