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Proof step 42 from proof maxpath-array (previous step)

st[r -- i '] = refval(r0), maxpath(str, r, st) = 1 + # refs0, 0 ≤ i, i < st[r -- _length] .intval, is_array(str, r, st), # refs0 < maxpath(str, r0, st), validrefs(str, r ' + refs0, st[r -- _type] .type, st), 0 < st[r -- _length] .intval, maxpath(str, r, st) ≤ maxpath(str, r0, st) ⊦ # validrefset(str, r0, st) = 0, validrefset(str, r0, st) = ∅, # validrefset(str, r, st) = 0, validrefset(str, r, st) = ∅, junkref(str, r, st), cyclic(str, r, st), dups(refs0), r ∈ refs0, has_reffield((r ' + refs0) .last, st)

User applied rule insert lemma

And obtained the following new goals

Proof step 5:
⊦ validrefset(str, r, st) ≠ ∅ → (∃ refs. refs ∈ validrefset(str, r, st) ∧ maxpath(str, r, st) = # refs)
Proof step 41:
validrefset(str, r0, st) ≠ ∅ → (∃ refs. refs ∈ validrefset(str, r0, st) ∧ maxpath(str, r0, st) = # refs), st[r -- i '] = refval(r0), maxpath(str, r, st) = 1 + # refs0, 0 ≤ i, i < st[r -- _length] .intval, is_array(str, r, st), # refs0 < maxpath(str, r0, st), validrefs(str, r ' + refs0, st[r -- _type] .type, st), 0 < st[r -- _length] .intval, maxpath(str, r, st) ≤ maxpath(str, r0, st) ⊦ # validrefset(str, r0, st) = 0, validrefset(str, r0, st) = ∅, # validrefset(str, r, st) = 0, validrefset(str, r, st) = ∅, junkref(str, r, st), cyclic(str, r, st), dups(refs0), r ∈ refs0, has_reffield((r ' + refs0) .last, st)

Rule argument

[LEMMAARG : maxpath-in, [str, r, st] → [str, r0, st]]

Additional information

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