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Proof step 18 from proof junkrefs-put-norefval-01 (previous step)

okval(val, ty0), is_obj(str, r, st[r1 -- mkfs(class, ty0, fieldvar) ', val]), st[r -- _type] .type ≤ ty, is_obj(str, r, st), mkfs(class1, ty3, fieldvar1) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r1 -- mkfs(class, ty0, fieldvar) ', val][r -- mkfs(class1, ty3, fieldvar1) ']), junkrefs (str, (st[r1 -- mkfs(class, ty0, fieldvar) ', val][r -- mkfs(class1, ty3, fieldvar1) ']) .refval ' + refs, ty3, st[r1 -- mkfs(class, ty0, fieldvar) ', val]), ∀ val0, ty1, str0, ty2, st0, r0, class0, fieldvar0. okval(val0, ty1) ∧ junkrefs (str0, (st[r1 -- mkfs(class, ty0, fieldvar) ', val][r -- mkfs(class1, ty3, fieldvar1) ']) .refval ' + refs, ty2, st0[r0 -- mkfs(class0, ty1, fieldvar0) ', val0]) → ty1 = void_type ∨ mkfs(class0, ty1, fieldvar0) ' = _length ∨ is_referencevalue(val0) ∨ junkrefs(str0, (st[r1 -- mkfs(class, ty0, fieldvar) ', val][r -- mkfs(class1, ty3, fieldvar1) ']) .refval ' + refs, ty2, st0) ⊦ r = jvmref, mkfs(class, ty0, fieldvar) ' = _length, ty0 = void_type, is_referencevalue(val), junkrefs(str, r ' + (st[r1 -- mkfs(class, ty0, fieldvar) ', val][r -- mkfs(class1, ty3, fieldvar1) ']) .refval ' + refs, ty, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
(st[r1 -- mkfs(class, ty0, fieldvar) ', val][r -- mkfs(class1, ty3, fieldvar1) ']) = refval(r2), okval(val, ty0), is_obj(str, r, st[r1 -- mkfs(class, ty0, fieldvar) ', val]), st[r -- _type] .type ≤ ty, is_obj(str, r, st), mkfs(class1, ty3, fieldvar1) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r1 -- mkfs(class, ty0, fieldvar) ', val][r -- mkfs(class1, ty3, fieldvar1) ']), junkrefs(str, r2 ' + refs, ty3, st[r1 -- mkfs(class, ty0, fieldvar) ', val]), ∀ val0, ty1, str0, ty2, st0, r0, class0, fieldvar0. okval(val0, ty1) ∧ junkrefs(str0, r2 ' + refs, ty2, st0[r0 -- mkfs(class0, ty1, fieldvar0) ', val0]) → ty1 = void_type ∨ mkfs(class0, ty1, fieldvar0) ' = _length ∨ is_referencevalue(val0) ∨ junkrefs(str0, r2 ' + refs, ty2, st0) ⊦ r = jvmref, mkfs(class, ty0, fieldvar) ' = _length, ty0 = void_type, is_referencevalue(val), junkrefs(str, r ' + r2 ' + refs, ty, st)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r1 -- mkfs(class, ty0, fieldvar) ', val] [r -- mkfs(class1, ty3, fieldvar1) ' ], r2] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r1 -- mkfs(class, ty0, fieldvar) ', val] [r -- mkfs(class1, ty3, fieldvar1) ' ], r2)]]