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Proof step 16 from proof cyclic-def-object (previous step)

refs1 = r0 + refs, r0 = st[r -- mkfs(class, ty, fieldvar) '] .refval, st[r -- _type] .type ≤ mkclasstype(`java.lang.Object' .class), is_obj(str, r, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty, fieldvar) ']), validrefs(str, refs1, ty, st) ⊦ r = jvmref, refs1 = [], ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ r0 = st[r -- fs '] .refval ∧ validrefs(str, refs1, fs .type, st), ¬ r ∈ refs1 ∧ ¬ dups(refs1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
st[r -- _type] .type ≤ mkclasstype(`java.lang.Object' .class), is_obj(str, r, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty, fieldvar) ']), validrefs(str, st[r -- mkfs(class, ty, fieldvar) '] .refval ' + refs, ty, st) ⊦ r = jvmref, ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- mkfs(class, ty, fieldvar) '] .refval = st[r -- fs '] .refval ∧ validrefs(str, st[r -- mkfs(class, ty, fieldvar) '] .refval ' + refs, fs .type, st), r ≠ st[r -- mkfs(class, ty, fieldvar) '] .refval ∧ ¬ r ∈ refs ∧ ¬ st[r -- mkfs(class, ty, fieldvar) '] .refval ∈ refs ∧ ¬ dups(refs)

Rule argument

[emptyarg]

Additional information

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