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Proof step 134 from proof cyclic-pseq (previous step)

st1[r1 -- _type] .type = mkclasstype(class), st[refs .first -- _type] = st1[r1 -- _type], is_obj(str, r1, st1), validrefs(str, refs + r0 ', mkclasstype(class), st), r0 ∈ refs, ∀ fs. fs ' ∈ instfields(class) ∧ is_referencevalue(st[refs .first -- fs ']) → ps=(st[refs .first -- fs '] .refval, st, st1[r1 -- fs '] .refval, st1), ∀ fs. fs ' ∈ instfields(class) ∧ ¬ is_referencevalue(st[refs .first -- fs ']) → st[refs .first -- fs '] = st1[r1 -- fs '], ∀ st, r, st0, r0, str0. maxpath(str0, r0, st0) < maxpath(str, r1, st1) → (ps=(r, st, r0, st0) ∧ cyclic(str0, r, st) → junkref(str0, r, st) ∨ junkref(str0, r0, st0) ∨ cyclic(str0, r0, st0)) ⊦ refs .first = jvmref, r1 = jvmref, dups(refs), cyclic(str, r1, st1), junkref(str, r1, st1), junkref(str, refs .first, st)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 133:
refs = r2 + refs0 ∧ refs ≠ [], st1[r1 -- _type] .type = mkclasstype(class), st[r2 -- _type] = st1[r1 -- _type], is_obj(str, r1, st1), validrefs(str, refs + r0 ', mkclasstype(class), st), r0 ∈ refs, ∀ fs. fs ' ∈ instfields(class) ∧ is_referencevalue(st[r2 -- fs ']) → ps=(st[r2 -- fs '] .refval, st, st1[r1 -- fs '] .refval, st1), ∀ fs. fs ' ∈ instfields(class) ∧ ¬ is_referencevalue(st[r2 -- fs ']) → st[r2 -- fs '] = st1[r1 -- fs '], ∀ st, r, st0, r0, str0. maxpath(str0, r0, st0) < maxpath(str, r1, st1) → (ps=(r, st, r0, st0) ∧ cyclic(str0, r, st) → junkref(str0, r, st) ∨ junkref(str0, r0, st0) ∨ cyclic(str0, r0, st0)) ⊦ r2 = jvmref, r1 = jvmref, dups(refs), cyclic(str, r1, st1), junkref(str, r1, st1), junkref(str, r2, st)

Rule argument

[speclemmaarg: ,refs ≠ [] → (r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0) ,[refs, r, refs0] → [refs, r2, refs0] ,T ,list-data ,references-olista ,elim-1 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ [] + refs = refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ ¬ r ∈ []], [CSIMPELIM : ⊦ refs ≠ [] → ( r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0)])], [EXTRATERMS : (refs, r2, refs0)]]