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Proof step 32 from proof maxpath-object (previous step)

r ' + r0 ' + refs1 ∈ validrefset(str, r, st), maxpath(str, r0, st) = 1 + # refs1, st[r -- fs '] = refval(r0), maxpath(str, r, st) = 2 + # refs, validrefs(str, r0 ' + refs1, 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 < # refs1, is_valid_ref(str, r0, st) ⊦ validrefset(str, r, st) = ∅, # validrefset(str, r, st) = 0, r = r1, validrefset(str, r0, st) = ∅, # validrefset(str, r0, st) = 0, refs1 = [], junkref(str, r, st), cyclic(str, r, st), has_reffield(r1, st), r ∈ refs, r1 ∈ refs, dups(refs), r0 ∈ refs1, dups(refs1), has_reffield(refs1 .last, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
r ' + r0 ' + refs1 ∈ validrefset(str, r, st), maxpath(str, r0, st) = 1 + # refs1, st[r -- fs '] = refval(r0), maxpath(str, r, st) = 2 + # refs, validrefs(str, r0 ' + refs1, 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 < # refs1, is_valid_ref(str, r0, st) ⊦ validrefset(str, r, st) = ∅, # validrefset(str, r, st) = 0, r = r1, validrefset(str, r0, st) = ∅, # validrefset(str, r0, st) = 0, refs1 = [], junkref(str, r, st), cyclic(str, r, st), has_reffield(r1, st), r ∈ refs, r1 ∈ refs, dups(refs), r0 ∈ refs1, dups(refs1), has_reffield(refs1 .last, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]