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Proof step 33 from proof validrefs-maxlen (previous step)

0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), # st .refs ≤ # refs, st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st), ∀ str0, ty0, st0. validrefs(str0, st[r -- i '] .refval ' + refs, ty0, st0) → # refs ≤ # st0 .refs ⊦ r = jvmref, r = st[r -- i '] .refval, dups(refs), st[r -- i '] .refval ∈ refs, r ∈ refs

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
st[r -- i '] = refval(r0), 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), # st .refs ≤ # refs, st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, r0 ' + refs, st[r -- _type] .type .type, st), ∀ str0, ty0, st0. validrefs(str0, r0 ' + refs, ty0, st0) → # refs ≤ # st0 .refs ⊦ r = jvmref, r = r0, dups(refs), r0 ∈ refs, r ∈ refs

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)]]