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Theorem nonnullrefs-in

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

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 3
Proof steps: 14
Used lemmas: getvals-rec-01,
Used spec theorems:
- assoclist/fieldinit/assoc-no
- valuesfuns/nonnullrefs-no
Used simplifier rules:
- javavalue/test-19
- javavalue/elim-13
- list/references/c
- valuesfuns/nonnullrefs-yes
- assoclist/fieldinit/inkeys-n
- list/references/a
- list/references/in-06
- list/javavalues/a
- valuesfuns/nonnullrefs-ok
- assoclist/fieldinit/infirst
- assoclist/fieldinit/assoc-yes
- pair/fieldinit/elim
- list/fieldinit-assoclista/a
- list/fieldinit-assoclista/c
- assoclist/fieldinit/empty