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Proof step 37 from proof validrefs-append (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, r ' + refs0, ty0, st), is_array(str, r0, st), ∀ str, r, refs0, ty0, st, ty. validrefs(str, r ' + refs0, ty0, st) ∧ validrefs(str, acc + r ', ty, st) → validrefs(str, acc + r ' + refs0, ty, st) ⊦ r0 = jvmref, validrefs(str, (r0 ' + acc) + r ' + refs0, ty, 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 36:
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, r ' + refs0, ty0, st), is_array(str, r0, st), ∀ str, r, refs0, ty0, st, ty. validrefs(str, r ' + refs0, ty0, st) ∧ validrefs(str, acc + r ', ty, st) → validrefs(str, acc + r ' + refs0, ty, st) ⊦ r0 = jvmref, validrefs(str, (r0 ' + acc) + r ' + refs0, ty, 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)]]