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Proof step 111 from proof validrefs-lastelem (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 110:
st[r0 -- i '] = refval(r1), acc + r ' = r1 ' + refs, 0 < st[r0 -- _length] .intval, 0 ≤ i, validrefs(str, acc + r ', st[r0 -- _type] .type .type, st), is_referencevalue(st[r0 -- i ']), i < st[r0 -- _length] .intval, st[r0 -- _type] .type ≤ ty, validrefs(str, r0 ' + acc, ty, st), is_array(str, r0, st), ∀ str, ty, st, r. validrefs(str, acc, ty, st) ∧ validrefs(str, acc + r ', ty, st) → acc = [] ∨ has_reffield(acc .last, st) ⊦ r0 = jvmref, has_reffield((r0 ' + acc) .last, st), r ≠ r1 ∧ ¬ r ∈ refs, ¬ r1 ∈ acc ∧ r1 ≠ r

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)]]