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Proof step 81 from proof validrefs-del-junkrefs (previous step)

0 < st[r0 -- _length] .intval, 0 ≤ i, junkrefs(str, (st[r0 -- i '] .refval ' + acc) + r ', st[r0 -- _type] .type .type, st -- r), is_referencevalue(st[r0 -- i ']), i < st[r0 -- _length] .intval, st[r0 -- _type] .type ≤ ty, is_array(str, r0, st), ∀ st, r0, ty, str, r. st[r0 -- _type] .type ≤ ty ∧ junkrefs(str, (r0 ' + acc) + r ', ty, st -- r) → r = r0 ∨ junkref(str, r0, st) ∨ r ∈ acc ∨ validrefs(str, r0 ' + acc + r ', ty, st) ⊦ r0 = jvmref, r = st[r0 -- i '] .refval, r = r0, validrefs(str, r0 ' + (st[r0 -- i '] .refval ' + acc) + r ', ty, st), r ∈ acc, junkref(str, r0, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 80:
st[r0 -- i '] = refval(r1), 0 < st[r0 -- _length] .intval, 0 ≤ i, junkrefs(str, (r1 ' + acc) + r ', st[r0 -- _type] .type .type, st -- r), is_referencevalue(st[r0 -- i ']), i < st[r0 -- _length] .intval, st[r0 -- _type] .type ≤ ty, is_array(str, r0, st), ∀ st, r0, ty, str, r. st[r0 -- _type] .type ≤ ty ∧ junkrefs(str, (r0 ' + acc) + r ', ty, st -- r) → r = r0 ∨ junkref(str, r0, st) ∨ r ∈ acc ∨ validrefs(str, r0 ' + acc + r ', ty, st) ⊦ r0 = jvmref, r = r1, r = r0, validrefs(str, r0 ' + (r1 ' + acc) + r ', ty, st), r ∈ acc, junkref(str, r0, st)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r0 -- i '], r1] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r0 -- i '], r1)]]