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Proof step 57 from proof maxpath-object (previous step)

refs0 = r0 + refs1, maxpath(str, r, st) = 2 + # refs, st[r -- fs '] = refval(r0), maxpath(str, r0, 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[r0 -- _type] .type, st), is_valid_ref(str, r0, st) ⊦ refs0 = [], # validrefset(str, r0, st) = 0, validrefset(str, r0, 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
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 : ([CSIMPSEQ : ⊦ refs ≠ [] → (r ' + refs) .last = refs .last], [CSIMPSEQ : ⊦ # refs = 0 ↔ refs = []], [CSIMPFORWARD : ⊦ # refsset ≠ 0 → refsset ≠ ∅], [CSIMPFORWARD : ⊦ refsset ≠ ∅ → # refsset ≠ 0], [CSIMPFORWARD : ⊦ m < n → n ≠ 0], [CSIMPSEQ : ⊦ dups(r ' + refs) ↔ dups(refs) ∨ r ∈ refs], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n < m + n0 ↔ n < n0], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ # (refs + refs0) = # refs + # refs0], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]