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Proof step 46 from proof maxpath-object (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
maxpath(str, r, st) = 2 + # refs, st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), maxpath(str, r0, st) = 1 + # refs1, is_valid_ref(str, r0, st), # refs < # refs1, is_obj(str, r, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str, r ' + refs + r1 ', st[r -- _type] .type, st), maxpath(str, r, st) ≤ maxpath(str, r0, st), validrefs(str, r0 ' + refs1, st[r0 -- _type] .type, st) ⊦ refs1 = [], # validrefset(str, r0, st) = 0, validrefset(str, r0, st) = ∅, r = r1, # validrefset(str, r, st) = 0, validrefset(str, r, st) = ∅, has_reffield(refs1 .last, st), dups(refs1), r0 ∈ refs1, dups(refs), r1 ∈ refs, r ∈ refs, has_reffield(r1, st), cyclic(str, r, st), junkref(str, r, st), validrefs(str, r0 ' + refs1, ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]