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Theorem nonnullrefs-dups-key

⊦ ¬ dups(fis .keys) → (dups(fis .vals .nonnullrefs) ↔ (∃ r, sk, sk0. sk ≠ sk0 ∧ r ≠ jvmref ∧ fis[sk] = refval(r) ∧ fis[sk0] = refval(r) ∧ sk ∈ fis ∧ sk0 ∈ fis))

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 11
Proof steps: 26
Used lemmas: nonnullrefs-in-key, keys-notin-02, getkeys-one, getkeys-app, getvals-rec-01, getvals-empty, nonnullrefs-dups,
Used spec theorems:
- valuesfuns/nonnullrefs-one-no
- assoclist/fieldinit/assoc-no
Used simplifier rules:
- list/references/Nil
- assoclist/fieldinit/assoc-no
- assoclist/fieldinit/assoc-yes
- javavalue/inj-03
- javavalue/test-19
- javavalue/elim-13
- list/references/a
- list-dup/references/rec
- valuesfuns/nonnullrefs-one-yes
- assoclist/fieldinit/inone
- pair/fieldinit/elim
- assoclist/fieldinit/in-append
- list/storekeys/a
- list-dup/storekeys/dups-cons
- list/javavalues/a
- valuesfuns/nonnullrefs-append
- list/fieldinit-assoclista/a
- list/fieldinit-assoclista/c
- valuesfuns/nonnullrefs-empty
- list-dup/references/e-01