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Proof step 17 from proof cyclic-def-object (previous step)

refs1 .first = 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 ']) ∧ refs1 .first = st[r -- fs '] .refval ∧ validrefs(str, refs1, fs .type, st), ¬ r ∈ refs1 ∧ ¬ dups(refs1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 16:
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)

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [refs1, r0, refs] ,T ,list-data ,references-olista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs1, r0, refs)]]