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Proof step 45 from proof cyclic-addobj (previous step)

refs0 = r1 + refs, fis .keys = instfields(class), r1 = (addobj(r, class, fis, st)[r -- mkfs(class0, ty, fieldvar) ']) .refval, 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, refs0, ty, addobj(r, class, fis, st)), ∀ fs, r0. fs ' × refval(r0) ∈ fis → ¬ junkref(str, r0, st) ∧ ¬ cyclic(str, r0, st) ⊦ refs0 = [], r = jvmref, ¬ r ∈ refs0 ∧ ¬ dups(refs0), ∃ fs. fs ' ∈ fis ∧ fs ' ∈ instfields(class) ∧ fis[fs '] = refval(r)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ dups(r ' + refs) ↔ ¬ ¬ (r ∈ refs ∨ dups(refs))], [CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]