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Theorem cyclic-def-simple

⊦ 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-addarray-noreftype, cyclic-addarray-other, cyclic-addarray-this, cyclic-addarray-this-01, cyclic-addobj, cyclic-addobj-other, cyclic-addobj-other-01, cyclic-addrefarray, cyclic-array, cyclic-class, cyclic-def-shortest, cyclic-delete, cyclic-not-null, cyclic-one, cyclic-put-statfield, cyclic-put-statfield-01, cyclic-putbyte, cyclic-putbyte-01, cyclic-subset, cyclic-subset-01, exvalidrefs, exvalidrefs-03, exvalidrefs-maxlength, exvalidrefs-nodups, pathex-put-cyclic,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 17
Proof steps: 45
Used lemmas: validrefs-array, validrefs-is-junk, validrefs-null, cyclic-def, cyclic-def-object,
Used spec theorems:
- Used simplifier rules:
  - int-abs/lels-04
  - int-abs/lels-03
  - javavalue/sel-09
  - javavalue/test-19
  - javavalue/elim-13
  - list/references/in-17
  - list/references/in-append
  - int-abs/forward-le-01
  - int-abs/forward-le-05
  - int-abs/lels
  - int-abs/lels-01
  - typefuns/ref
  - list/references/c-08
  - list-dup/references/dups-cons
  - addfuns/isarray-isobj-01
  - okfuns/is_array-typele
  - addfuns/is_valid_ref
  - addfuns/is_obj-null
  - list/references/in-empty
  - 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