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Proof step 14 from proof cyclic-class (previous step)

st[r -- mkfs(class, ty, fieldvar) '] = refval(refs .first), st[refs .first -- _type] .type ≤ ty, is_reftype(ty), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), dups(refs), validrefs(str, refs, st[refs .first -- _type] .type, st) ⊦ ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[refs .first -- _type] .type, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
refs = r0 + refs0 ∧ refs ≠ [], st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), st[r0 -- _type] .type ≤ ty, is_reftype(ty), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), dups(refs), validrefs(str, refs, st[r0 -- _type] .type, st) ⊦ ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[refs .first -- _type] .type, st)

Rule argument

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

Additional information

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