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Theorem nonnullrefs-dups

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

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: nonnullrefs-dups-key,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 8
Proof steps: 20
Used lemmas: nonnullrefs-in, getvals-rec-01,
Used spec theorems:
- valuesfuns/nonnullrefs-no
- assoclist/fieldinit/assoc-no
Used simplifier rules:
- javavalue/sel-09
- assoclist/fieldinit/assoc-no
- assoclist/fieldinit/assoc-yes
- javavalue/inj-03
- assoclist/fieldinit/inkeys-n
- assoclist/fieldinit/infirst
- javavalue/test-19
- javavalue/elim-13
- list/references/a
- list-dup/references/dups-cons
- list/javavalues/a
- list/references/c
- valuesfuns/nonnullrefs-yes
- pair/fieldinit/elim
- list/fieldinit-assoclista/a
- list/fieldinit-assoclista/c
- assoclist/fieldinit/empty