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Proof step 35 from proof maxpath-array (previous step)

st[r -- i '] = refval(r0), maxpath(str, r, st) = 1 + # refs0, maxpath(str, r0, st) = 1 + # refs1, is_valid_ref(str, r0, st), maxpath(str, r, st) ≤ maxpath(str, r0, st), 0 ≤ i, i < st[r -- _length] .intval, is_array(str, r, st), # refs0 ≤ # refs1, validrefs(str, r ' + refs0, st[r -- _type] .type, st), 0 < st[r -- _length] .intval, validrefs(str, r0 ' + refs1, st[r0 -- _type] .type, st) ⊦ r ' + r0 ' + refs1 ∈ validrefset(str, r, 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), has_reffield((r0 ' + refs1) .last, st), dups(refs1), r0 ∈ refs1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ 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 34:
is_valid_ref(str, r, st), st[r -- i '] = refval(r0), maxpath(str, r, st) = 1 + # refs0, maxpath(str, r0, st) = 1 + # refs1, is_valid_ref(str, r0, st), maxpath(str, r, st) ≤ maxpath(str, r0, st), 0 ≤ i, i < st[r -- _length] .intval, is_array(str, r, st), # refs0 ≤ # refs1, validrefs(str, r ' + refs0, st[r -- _type] .type, st), 0 < st[r -- _length] .intval, validrefs(str, r0 ' + refs1, st[r0 -- _type] .type, st) ⊦ r ' + r0 ' + refs1 ≠ [] ∧ (r ' + r0 ' + refs1) .first = r ∧ ¬ has_reffield((r ' + r0 ' + refs1) .last, st) ∧ ¬ dups(r ' + r0 ' + refs1) ∧ validrefs(str, r ' + r0 ' + refs1, st[r -- _type] .type, 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), has_reffield((r0 ' + refs1) .last, st), dups(refs1), r0 ∈ refs1

Rule argument

[crewrite-arg: validrefset-def , F , [st, r, str, refs] → [st, r, str, r ' + r0 ' + refs1] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_valid_ref(str, r, st) → ( validrefs (str, r ' + refs, ty, st) ↔ r = jvmref ∧ refs = [])], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ is_array(str, r, st) → is_valid_ref(str, r, st)])], [EXTRATERMS : (st, r, str, r ' + r0 ' + refs1)]]