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Proof step 48 from proof maxpath-array (previous step)

st[r -- i '] = refval(r0), maxpath(str, r, st) = # refs, 0 < st[r -- _length] .intval, 0 ≤ i, i < st[r -- _length] .intval, is_array(str, r, st), maxpath(str, r, st) ≤ maxpath(str, r0, st), refs ∈ validrefset(str, r, st) ⊦ # validrefset(str, r, st) = 0, validrefset(str, r, st) = ∅, junkref(str, r, st), cyclic(str, r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 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))
Proof step 47:
is_valid_ref(str, r, st), st[r -- i '] = refval(r0), maxpath(str, r, st) = # refs, 0 < st[r -- _length] .intval, 0 ≤ i, i < st[r -- _length] .intval, is_array(str, r, st), maxpath(str, r, st) ≤ maxpath(str, r0, st), refs ≠ [] ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st) ∧ ¬ dups(refs) ∧ validrefs(str, refs, st[r -- _type] .type, st) ⊦ # validrefset(str, r, st) = 0, validrefset(str, r, st) = ∅, junkref(str, r, st), cyclic(str, r, st)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_array(str, r, st) → is_valid_ref(str, r, st)])], [EXTRATERMS : (st, r, str, refs)]]