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Proof step 71 from proof maxpath-object (previous step)

is_valid_ref(str, r, st), st[r -- fs '] = refval(r0), maxpath(str, r, st) = # refs, maxpath(str, r, st) ≤ maxpath(str, r0, st), is_obj(str, r, st), fs ' ∈ instfields(st[r -- _type] .type .class), 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) = ∅, cyclic(str, r, st), junkref(str, r, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 70:
st[refs .first -- fs '] = refval(r0), maxpath(str, refs .first, st) = # refs, # refs ≤ maxpath(str, r0, st), is_obj(str, refs .first, st), fs ' ∈ instfields(st[refs .first -- _type] .type .class), validrefs(str, refs, st[refs .first -- _type] .type, st) ⊦ # validrefset(str, refs .first, st) = 0, validrefset(str, refs .first, st) = ∅, refs = [], cyclic(str, refs .first, st), junkref(str, refs .first, st), dups(refs), has_reffield(refs .last, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ # refsset ≠ 0 → refsset ≠ ∅], [CSIMPFORWARD : ⊦ refsset ≠ ∅ → # refsset ≠ 0], [CSIMPSEQ : ⊦ is_obj(str, r, st) → is_valid_ref(str, r, st)])]]