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

st2[r -- i '] = st[r -- i '], st[r -- _type] = st1[r1 -- _type], st2[r -- _type] = st1[r1 -- _type], st[r -- _length] .intval = st1[r1 -- _length] .intval, st2[r -- _length] .intval = st1[r1 -- _length] .intval, st1[st1[r1 -- i '] .refval -- _type] .type = st1[r1 -- _type] .type .type, st[st[r -- i '] .refval -- _type] .type = st1[r1 -- _type] .type .type, is_referencevalue(st1[r1 -- i ']), r -- i ' ∈ st2, r -- i ' ∈ st, ps=(st[r -- i '] .refval, st, st1[r1 -- i '] .refval, st1), 0 < st1[r1 -- _length] .intval, 0 ≤ i, is_arraytype(st1[r1 -- _type] .type), r ∈ st2, r ∈ st, r -- _type ∈ st2, r -- _type ∈ st, is_array(str, r1, st1), is_array(str, r, st), is_referencevalue(st[r -- i ']), i < st1[r1 -- _length] .intval, ∀ i. ¬ i < 0 ∧ ¬ st1[r1 -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) → ps=(st[r -- i '] .refval, st, st1[r1 -- i '] .refval, st1), ∀ i. ¬ i < 0 ∧ ¬ st1[r1 -- _length] .intval ≤ i ∧ ¬ is_referencevalue(st[r -- i ']) → st[r -- i '] = st1[r1 -- i '], ∀ rk. rk ∈ st → rk ∈ st2 ∧ st[rk] = st2[rk], cyclic(str, st[r -- i '] .refval, st) ∨ cyclic(str, st1[r1 -- i '] .refval, st1), ∀ st1, r1, st2, st0, r0, str0. maxpath(str0, r0, st0) < maxpath(str, r, st) → ( st0 ⊆ st2 ∧ ps=(r0, st0, r1, st1) → junkref(str0, r0, st0) ∨ cyclic(str0, r0, st0) ∨ junkref(str0, r1, st1) ∨ cyclic(str0, r1, st1) ∨ ps=(r0, st2, r1, st1)) ⊦ r = jvmref, r1 = jvmref, st1[r1 -- i '] .refval = jvmref, st[r -- i '] .refval = jvmref, is_reftype(st1[r1 -- _type] .type .type), cyclic(str, r, st), cyclic(str, r1, st1), ps=(st[r -- i '] .refval, st2, st1[r1 -- i '] .refval, st1), junkref(str, st1[r1 -- i '] .refval, st1), junkref(str, st[r -- i '] .refval, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , is_referencevalue(st[r -- i ']) ∧ ¬ is_reftype(st[r -- _type] .type .type) ∧ 0 ≤ i ∧ i < st[r -- _length] .intval → ¬ is_array(str, r, st) ,[st, r, i, str] → [st, r, i, str] ,F ,okfuns , ,is_array-noreftype ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_referencevalue(st[r -- i ']) ∧ ¬ is_reftype (st[r -- _type] .type .type) ∧ 0 ≤ i ∧ i < st[r -- _length] .intval → ¬ is_array(str, r, st)])], [EXTRATERMS : (st, r, i, str)]]