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Proof step 216 from proof cyclic-pseq (previous step)

(refs0 + r0 ') .first = st[r2 -- i '] .refval, st[r2 -- _length] .intval = st1[r1 -- _length] .intval, st[r2 -- _type] = st1[r1 -- _type], 0 < st1[r1 -- _length] .intval, 0 ≤ i, validrefs(str, refs0 + r0 ', st1[r1 -- _type] .type .type, st), is_referencevalue(st[r2 -- i ']), i < st1[r1 -- _length] .intval, is_array(str, r1, st1), is_array(str, r2, st), is_arraytype(st1[r1 -- _type] .type), ps=((refs0 + r0 ') .first, 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 '], junkref(str, (refs0 + r0 ') .first, st) ∨ junkref(str, st1[r1 -- i '] .refval, st1), ∀ 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)) ⊦ r1 = jvmref, r2 = jvmref, is_reftype(st1[r1 -- _type] .type .type), cyclic(str, st1[r1 -- i '] .refval, st1), r2 ∈ refs0, dups(refs0), cyclic(str, r1, st1), r0 ≠ r2 ∧ ¬ r0 ∈ refs0, (refs0 + r0 ') .first ≠ jvmref ∧ (st[(refs0 + r0 ') .first -- _type] .type ≠ st1[r1 -- _type] .type .type ∨ junkref(str, (refs0 + r0 ') .first, st)), is_referencevalue(st1[r1 -- i ']) ∧ st1[r1 -- i '] .refval ≠ jvmref ∧ (st1[st1[r1 -- i '] .refval -- _type] .type ≠ st1[r1 -- _type] .type .type ∨ junkref(str, st1[r1 -- i '] .refval, st1))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , ¬ is_reftype(ty) → (validrefs(str, refs, ty, st) ↔ refs = [] ∨ refs = jvmref ') ,[st, ty, refs, str] → [st, st1[r1 -- _type] .type .type, refs0 + r0 ', str] ,F ,cyclic , ,validrefs-primtype ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' = refs + r0 ' ↔ r = r0 ∧ refs = []], [CSIMPSEQ : ⊦ r ∈ refs → (refs + refs0) .first = refs .first], [CSIMPSEQ : ⊦ ¬ r ∈ []])], [EXTRATERMS : (st, st1[r1 -- _type] .type .type, refs0 + r0 ', str)]]