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Theorem addarray-disjoint-nosharing

⊦ disjoint(str, refs, st) ∧ ¬ hasSharing(refs, st) ∧ ¬ dups(refs) ∧ validreflist(str, mkjavavalues(refs), ty, st) ∧ newref(r, st) → ¬ hasSharing(r, addarray(r, ty, mkjavavalues(refs), st))

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: 37
Proof steps: 83
Used lemmas: fits-null, disjoint-def-fits, hasSharing-def-better, hasSharing-list-def, fits-storekeys-empty, fits-in, fits-subset-01, fits-rec, hasSharing-def,
Used spec theorems:
Used simplifier rules:
- junkrefs/junkref-null
- typefuns/subtype-object-01
- int-abs/zero-gels-04
- list/storekeys/app-01
- oelem/intlista/lel
- intnat/abs-eq
- list-del/references/get-nodups
- storefuns/lookup-empty
- list/storekeys/app
- storefuns/lookup-one
- storefuns/instore-empty
- junkrefs/junkref-notin
- list-del/references/get-in
- junkrefs/validref-junkref
- addarray/addarray-subset
- javavalue/sel-09
- valuesfuns/mkvalsr-at
- intnat/inni-ls
- list/storekeys/c-07
- list/storekeys/c-08
- list/storekeys/app-02-ant
- list/storekeys/e
- nat-basic1/one
- int-basic1/forward-pos
- oelem/intlista/transitivity
- int-abs/absle
- intnat/labs
- nat/fle
- nat-basic1/f
- javavalue/inj-03
- nat/lels
- int-abs/lels-01
- int-abs/lels-04
- int-abs/lels
- int-abs/lels-03
- javavalue/elim-13
- storekey/test-08
- storekey/elim-04
- list/storekeys/a
- list/storekeys/e-01
- list/storekeys/c
- list-data/storekeys/elim-list-c
- list-data/references/l
- nat-basic1/z
- intnat/num-n2i-ls-02
- int-abs/forward-le-01
- int-abs/forward-le-05
- javavalue/sel-04
- valuesfuns/mkvalsr-len
- addarray/length-1init-01
- javatype/test-09
- javatype/test-16
- javavalue/sel-11
- addarray/type-1init
- javavalue/test-19
- valuefuns/refval-xtra
- javavalue/elim-refval
- storefuns/newref-01