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Theorem cyclic-def-object

⊦ is_obj(str, r, st) → (cyclic(str, r, st) ↔ (∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[r -- _type] .type, st)))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: cyclic-def-simple,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 10
Proof steps: 30
Used lemmas: validrefs-class, validrefs-is-junk, validrefs-null, validrefs-sametype, cyclic-def,
Used spec theorems:
- Used simplifier rules:
  - fieldspec/sel-03
  - javavalue/sel-09
  - javavalue/test-19
  - javavalue/elim-13
  - list/references/in-17
  - list/references/in-append
  - addfuns/is_obj-typele
  - javavalue/elim-refval
  - fieldspec/elim
  - typefuns/ref
  - addfuns/is_valid_ref-isobj
  - addfuns/is_obj-null
  - list-dup/references/dups-cons
  - list/references/c-08
  - list-dup/references/rec
  - list/references/a
  - list/references/e-01
  - list/references/c
  - list-dup/references/e-01
  - list-data/references/elim-list-c