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Proof step 18 from proof junkrefs-put-badarrayfield (previous step)

is_obj(str, r, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, is_obj(str, r, st), is_arraytype(st[r0 -- _type] .type), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r0 -- fs ', val][r -- mkfs(class, ty1, fieldvar) ']), junkrefs(str, (st[r0 -- fs ', val][r -- mkfs(class, ty1, fieldvar) ']) .refval ' + refs, ty1, st[r0 -- fs ', val]), ∀ str0, ty0, st0, fs1, r1, val0. ¬ junkrefs(str0, (st[r0 -- fs ', val][r -- mkfs(class, ty1, fieldvar) ']) .refval ' + refs, ty0, st0) ∧ fs1 ' ≠ _type ∧ is_arraytype(st0[r1 -- _type] .type) ∧ fs1 ' ≠ _length → ¬ junkrefs(str0, (st[r0 -- fs ', val][r -- mkfs(class, ty1, fieldvar) ']) .refval ' + refs, ty0, st0[r1 -- fs1 ', val0]) ⊦ fs ' = _length, fs ' = _type, r = jvmref, junkrefs(str, r ' + (st[r0 -- fs ', val][r -- mkfs(class, ty1, fieldvar) ']) .refval ' + refs, ty, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
(st[r0 -- fs ', val][r -- mkfs(class, ty1, fieldvar) ']) = refval(r2), is_obj(str, r, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, is_obj(str, r, st), is_arraytype(st[r0 -- _type] .type), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r0 -- fs ', val][r -- mkfs(class, ty1, fieldvar) ']), junkrefs(str, r2 ' + refs, ty1, st[r0 -- fs ', val]), ∀ str0, ty0, st0, fs1, r1, val0. ¬ junkrefs(str0, r2 ' + refs, ty0, st0) ∧ fs1 ' ≠ _type ∧ is_arraytype(st0[r1 -- _type] .type) ∧ fs1 ' ≠ _length → ¬ junkrefs(str0, r2 ' + refs, ty0, st0[r1 -- fs1 ', 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[r0 -- fs ', val][r -- mkfs(class, ty1, fieldvar) '], r2] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r0 -- fs ', val][r -- mkfs(class, ty1, fieldvar) '], r2)]]