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Proof step 33 from proof junkrefs-put-badarrayfield (previous step)

0 ≤ i, 0 < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, is_array(str, r, st), is_arraytype(st[r0 -- _type] .type), i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), junkrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st[r0 -- fs ', val]), ∀ str0, ty0, st0, fs0, r1, val0. ¬ junkrefs(str0, st[r -- i '] .refval ' + refs, ty0, st0) ∧ fs0 ' ≠ _type ∧ is_arraytype(st0[r1 -- _type] .type) ∧ fs0 ' ≠ _length → ¬ junkrefs(str0, st[r -- i '] .refval ' + refs, ty0, st0[r1 -- fs0 ', val0]) ⊦ fs ' = _length, fs ' = _type, r = jvmref, junkrefs(str, r ' + st[r -- i '] .refval ' + refs, ty, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
st[r -- i '] = refval(r2), 0 ≤ i, 0 < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, is_array(str, r, st), is_arraytype(st[r0 -- _type] .type), i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), junkrefs(str, r2 ' + refs, st[r -- _type] .type .type, st[r0 -- fs ', val]), ∀ str0, ty0, st0, fs0, r1, val0. ¬ junkrefs(str0, r2 ' + refs, ty0, st0) ∧ fs0 ' ≠ _type ∧ is_arraytype(st0[r1 -- _type] .type) ∧ fs0 ' ≠ _length → ¬ junkrefs(str0, r2 ' + refs, ty0, st0[r1 -- fs0 ', val0]) ⊦ fs ' = _length, fs ' = _type, r = jvmref, junkrefs(str, r ' + r2 ' + refs, ty, st)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r -- i '], r2] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r -- i '], r2)]]