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Proof step 240 from proof cyclic-pseq (previous step)

st[refs .first -- _type] = st1[r1 -- _type], st[refs .first -- _length] .intval = st1[r1 -- _length] .intval, is_array(str, r1, st1), r0 ∈ refs, validrefs(str, refs + r0 ', st1[r1 -- _type] .type, st), is_arraytype(st1[r1 -- _type] .type), is_array(str, refs .first, st), ∀ i. ¬ i < 0 ∧ ¬ st1[r1 -- _length] .intval ≤ i ∧ is_referencevalue(st[refs .first -- i ']) → ps=(st[refs .first -- i '] .refval, st, st1[r1 -- i '] .refval, st1), ∀ i. ¬ i < 0 ∧ ¬ st1[r1 -- _length] .intval ≤ i ∧ ¬ is_referencevalue(st[refs .first -- i ']) → st[refs .first -- i '] = st1[r1 -- i '], ∀ 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, cyclic(str, r1, st1), junkref(str, r1, st1), junkref(str, refs .first, st), dups(refs)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 239:
refs = r2 + refs0 ∧ refs ≠ [], st[r2 -- _type] = st1[r1 -- _type], st[r2 -- _length] .intval = st1[r1 -- _length] .intval, is_array(str, r1, st1), r0 ∈ refs, validrefs(str, refs + r0 ', st1[r1 -- _type] .type, st), is_arraytype(st1[r1 -- _type] .type), is_array(str, r2, st), ∀ i. ¬ i < 0 ∧ ¬ st1[r1 -- _length] .intval ≤ i ∧ is_referencevalue(st[r2 -- i ']) → ps=(st[r2 -- i '] .refval, st, st1[r1 -- i '] .refval, st1), ∀ i. ¬ i < 0 ∧ ¬ st1[r1 -- _length] .intval ≤ i ∧ ¬ is_referencevalue(st[r2 -- i ']) → st[r2 -- i '] = st1[r1 -- i '], ∀ 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, cyclic(str, r1, st1), junkref(str, r1, st1), junkref(str, r2, st), dups(refs)

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