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Proof step 59 from proof maxpath-object (previous step)

is_valid_ref(str, r0, st), maxpath(str, r0, st) = # refs0, st[r -- fs '] = refval(r0), maxpath(str, r, st) = 2 + # refs, refs0 ≠ [] ∧ refs0 .first = r0 ∧ ¬ has_reffield(refs0 .last, st) ∧ ¬ dups(refs0) ∧ validrefs(str, refs0, st[r0 -- _type] .type, st), maxpath(str, r, st) ≤ maxpath(str, r0, st), validrefs(str, r ' + refs + r1 ', st[r -- _type] .type, st), fs ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), # refs + 1 < maxpath(str, r0, st) ⊦ validrefset(str, r, st) = ∅, # validrefset(str, r, st) = 0, r = r1, validrefset(str, r0, st) = ∅, # validrefset(str, r0, st) = 0, junkref(str, r, st), cyclic(str, r, st), has_reffield(r1, st), r ∈ refs, r1 ∈ refs, dups(refs)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 58:
maxpath(str, r, st) = 2 + # refs, st[r -- fs '] = refval(refs0 .first), maxpath(str, refs0 .first, st) = # refs0, # refs + 1 < # refs0, is_obj(str, r, st), fs ' ∈ instfields(st[r -- _type] .type .class), validrefs(str, r ' + refs + r1 ', st[r -- _type] .type, st), maxpath(str, r, st) ≤ # refs0, validrefs(str, refs0, st[refs0 .first -- _type] .type, st), is_valid_ref(str, refs0 .first, st) ⊦ refs0 = [], # validrefset(str, refs0 .first, st) = 0, validrefset(str, refs0 .first, st) = ∅, r = r1, # validrefset(str, r, st) = 0, validrefset(str, r, st) = ∅, has_reffield(refs0 .last, st), dups(refs0), dups(refs), r1 ∈ refs, r ∈ refs, has_reffield(r1, st), cyclic(str, r, st), junkref(str, r, 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])]]