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Proof step 44 from proof cyclic-addobj (previous step)

fis .keys = instfields(class), validfieldinits(fis, st), is_obj(str, r, addobj(r, class, fis, st)), newref(r, st), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), is_referencevalue(addobj(r, class, fis, st)[r -- mkfs(class0, ty, fieldvar) ']), validrefs(str, (addobj(r, class, fis, st)[r -- mkfs(class0, ty, fieldvar) ']) .refval ' + refs, ty, addobj(r, class, fis, st)), ∀ fs, r0. fs ' × refval(r0) ∈ fis → ¬ junkref(str, r0, st) ∧ ¬ cyclic(str, r0, st) ⊦ r = jvmref, ∃ fs. fs ' ∈ fis ∧ fs ' ∈ instfields(class) ∧ fis[fs '] = refval(r), r ≠ (addobj(r, class, fis, st)[r -- mkfs(class0, ty, fieldvar) ']) .refval ∧ ¬ r ∈ refs ∧ ¬ (addobj(r, class, fis, st)[r -- mkfs(class0, ty, fieldvar) ']) .refval ∈ refs ∧ ¬ dups(refs)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 43:
(addobj(r, class, fis, st)[r -- mkfs(class0, ty, fieldvar) ']) = refval(r1), fis .keys = instfields(class), validfieldinits(fis, st), is_obj(str, r, addobj(r, class, fis, st)), newref(r, st), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), is_referencevalue(addobj(r, class, fis, st)[r -- mkfs(class0, ty, fieldvar) ']), validrefs(str, r1 ' + refs, ty, addobj(r, class, fis, st)), ∀ fs, r0. fs ' × refval(r0) ∈ fis → ¬ junkref(str, r0, st) ∧ ¬ cyclic(str, r0, st) ⊦ r = jvmref, ∃ fs. fs ' ∈ fis ∧ fs ' ∈ instfields(class) ∧ fis[fs '] = refval(r), r ≠ r1 ∧ ¬ r ∈ refs ∧ ¬ r1 ∈ refs ∧ ¬ dups(refs)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [addobj(r, class, fis, st)[r -- mkfs(class0, ty, fieldvar) '], r1] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (addobj(r, class, fis, st) [r -- mkfs(class0, ty, fieldvar) ' ], r1)]]