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Proof step 39 from proof maxpath-array (previous step)

is_valid_ref(str, r0, st), maxpath(str, r0, st) = # refs, maxpath(str, r, st) = 1 + # refs0, st[r -- i '] = refval(r0), refs ≠ [] ∧ refs .first = r0 ∧ ¬ has_reffield(refs .last, st) ∧ ¬ dups(refs) ∧ validrefs(str, refs, st[r0 -- _type] .type, st), 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, validrefset(str, r0, st) = ∅, # validrefset(str, r0, st) = 0, has_reffield((r ' + refs0) .last, st), r ∈ refs0, dups(refs0), cyclic(str, r, st), junkref(str, r, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
st[r -- i '] = refval(refs .first), maxpath(str, r, st) = 1 + # refs0, maxpath(str, refs .first, st) = # refs, maxpath(str, r, st) ≤ # refs, 0 ≤ i, i < st[r -- _length] .intval, is_array(str, r, st), # refs0 < # refs, validrefs(str, r ' + refs0, st[r -- _type] .type, st), 0 < st[r -- _length] .intval, validrefs(str, refs, st[refs .first -- _type] .type, st), is_valid_ref(str, refs .first, st) ⊦ refs = [], # validrefset(str, refs .first, st) = 0, validrefset(str, refs .first, st) = ∅, # validrefset(str, r, st) = 0, validrefset(str, r, st) = ∅, has_reffield(refs .last, st), dups(refs), junkref(str, r, st), cyclic(str, r, st), dups(refs0), r ∈ refs0, has_reffield((r ' + refs0) .last, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # refs = 0 ↔ refs = []], [CSIMPFORWARD : ⊦ refsset ≠ ∅ → # refsset ≠ 0], [CSIMPFORWARD : ⊦ # refsset ≠ 0 → refsset ≠ ∅], [CSIMPFORWARD : ⊦ m < n → n ≠ 0], [CSIMPFORWARD : ⊦ m < n ∧ n = n0 → m < n0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPFORWARD : ⊦ m = n + 1 ∧ n < n0 → m ≤ n0])]]