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Proof step 58 from proof junkrefs-put-nopathex (previous step)

0 ≤ i, 0 < (st[r0 -- sk, val][r1 -- _length]) .intval, is_array(str, r1, st[r0 -- sk, val]), st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), i < (st[r0 -- sk, val][r1 -- _length]) .intval, is_referencevalue(st[r0 -- sk, val][r1 -- i ']), junkrefs(str, (st[r0 -- sk, val][r1 -- i ']) .refval ' + refs, st[r1 -- _type] .type .type, st[r0 -- sk, val]), ∀ str0, r, st0, ty0, sk0, val0. ¬ path∃(str0, (st[r0 -- sk, val][r1 -- i ']) .refval, r, st0) ∧ ¬ junkrefs(str0, (st[r0 -- sk, val][r1 -- i ']) .refval ' + refs, ty0, st0) ∧ sk0 ≠ _type → ¬ junkrefs(str0, (st[r0 -- sk, val][r1 -- i ']) .refval ' + refs, ty0, st0[r -- sk0, val0]) ⊦ sk = _type, r1 = jvmref, path∃(str, r1, r0, st), junkrefs(str, r1 ' + (st[r0 -- sk, val][r1 -- i ']) .refval ' + refs, ty, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 57:
(st[r0 -- sk, val][r1 -- i ']) = refval(r2), 0 ≤ i, 0 < (st[r0 -- sk, val][r1 -- _length]) .intval, is_array(str, r1, st[r0 -- sk, val]), st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), i < (st[r0 -- sk, val][r1 -- _length]) .intval, is_referencevalue(st[r0 -- sk, val][r1 -- i ']), junkrefs(str, r2 ' + refs, st[r1 -- _type] .type .type, st[r0 -- sk, val]), ∀ str0, r, st0, ty0, sk0, val0. ¬ path∃(str0, r2, r, st0) ∧ ¬ junkrefs(str0, r2 ' + refs, ty0, st0) ∧ sk0 ≠ _type → ¬ junkrefs(str0, r2 ' + refs, ty0, st0[r -- sk0, val0]) ⊦ sk = _type, r1 = jvmref, path∃(str, r1, r0, st), junkrefs(str, r1 ' + r2 ' + refs, ty, st)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r0 -- sk, val][r1 -- i '], r2] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r0 -- sk, val][r1 -- i '], r2)]]