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Proof step 44 from proof maxpath-array (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ validrefset(str, r, st) = ∅ → maxpath(str, r, st) = 0
Proof step 43:
validrefset(str, r0, st) ≠ ∅, maxpath(str, r, st) = 1 + # refs0, st[r -- i '] = refval(r0), maxpath(str, r, st) ≤ maxpath(str, r0, st), 0 < st[r -- _length] .intval, validrefs(str, r ' + refs0, st[r -- _type] .type, st), # refs0 < maxpath(str, r0, st), is_array(str, r, st), i < st[r -- _length] .intval, 0 ≤ i ⊦ validrefset(str, r, st) = ∅, # validrefset(str, r, st) = 0, has_reffield((r ' + refs0) .last, st), r ∈ refs0, dups(refs0), cyclic(str, r, st), junkref(str, r, st)

Rule argument

[crewrite-arg: maxpath-zero, F, [st, r, str] → [st, r0, str]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m ≤ 0 ↔ m = 0], [CSIMPSEQ : ⊦ ¬ n < 0])], [EXTRATERMS : (st, r0, str)]]