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Proof step 69 from proof maxpath-object (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 68:
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) ⊦ validrefset(str, r, st) = ∅, # validrefset(str, r, st) = 0, has_reffield((r ' + refs0) .last, st), r ∈ refs0, dups(refs0), junkref(str, r, st), cyclic(str, r, st)

Rule argument

[emptyarg]

Additional information

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