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Proof step 53 from proof validrefs-junkrefs-01 (previous step)

acc + refs0 = st[r -- i '] .refval ' + refs, 0 < st[r -- _length] .intval, 0 ≤ i, st[r -- _type] .type ≤ ty, junkrefs(str, acc + refs0, st[r -- _type] .type .type, st), is_referencevalue(st[r -- i ']), i < st[r -- _length] .intval, is_array(str, r, st), ∀ str, refs0, ty, st. junkrefs(str, acc + refs0, ty, st) → junkrefs(str, acc, ty, st) ∨ validrefs(str, acc, ty, st) ⊦ acc + refs0 = [], r = jvmref, validrefs(str, r ' + acc, ty, st), junkrefs(str, r ' + acc, ty, st), ¬ st[r -- i '] .refval ∈ acc ∧ ¬ st[r -- i '] .refval ∈ refs0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 52:
st[r -- i '] = refval(r0), acc + refs0 = r0 ' + refs, 0 < st[r -- _length] .intval, 0 ≤ i, st[r -- _type] .type ≤ ty, junkrefs(str, acc + refs0, st[r -- _type] .type .type, st), is_referencevalue(st[r -- i ']), i < st[r -- _length] .intval, is_array(str, r, st), ∀ str, refs0, ty, st. junkrefs(str, acc + refs0, ty, st) → junkrefs(str, acc, ty, st) ∨ validrefs(str, acc, ty, st) ⊦ acc + refs0 = [], r = jvmref, validrefs(str, r ' + acc, ty, st), junkrefs(str, r ' + acc, ty, st), ¬ r0 ∈ acc ∧ ¬ r0 ∈ refs0

Rule argument

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

Additional information

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