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Proof step 65 from proof maxpath-object (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 64:
st[r -- fs '] = refval(r0), maxpath(str, r, st) = 2 + # refs, 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, junkref(str, r, st), cyclic(str, r, st), has_reffield(r1, st), r ∈ refs, r1 ∈ refs, dups(refs)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ dups(refs + r ') ↔ r ∈ refs ∨ dups(refs)], [CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPSEQ : ⊦ refs + r ' ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ # (refs + refs0) = # refs + # refs0])]]