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Theorem in-add

⊦ r -- j ' ∈ addarray(r, ty, vals, st) ↔ r -- j ' ∈ st ∨ 0 ≤ j ∧ j < n→i(# vals)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: add-in-other, add-in-other-index, addarray-addaray, addarray-identity, addarray-put-01, addbar-okarray-01, isarray-init-01, isarray-init-02, okarray-addarray, okarray-init-05, okarray-putarray-addarray-put, putarray-add-same, putarray-addarray-01, putarray-addarray-one, putarray-addarray-override, union-addarray-rew,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 8
Proof steps: 18
Used lemmas: addarrayinit-base, addarrayinit-def, add-lastrec,
Used spec theorems:
- store/javastore/In-insert
Used simplifier rules:
- intnat/nat2int-08
- int-abs/forward-le-02
- int-abs/zero-gels-01
- int-abs/lels-03
- int-basic1/ls-01
- oelem/intlista/ls-le
- intnat/pos-int
- oelem/intlista/lel
- intnat/num-n2i-ls-02
- nat-basic1/z
- intnat/nat2int-04
- oelem/intlista/sls
- nat-basic2/s
- nat-basic1/ref-1
- storekey/inj-04
- refkey/inj
- list/javavalues/e-02
- nat-basic2/eq-01
- list/javavalues/a
- list/javavalues/len-02
- list/javavalues/len
- list-last/javavalues/last-elim
- int-basic2/add-c
- int-basic2/add-a
- int-abs/succ-01
- nat-basic2/c
- nat-basic2/a
- intnat/n2i-add
- list-data/javavalues/l
- nat/elim-pred-c
- nat/pred-03
- specialkeys/len
- javastore/instore-02
- specialkeys/type-03
- list-data/javavalues/size-01
- int-abs/lels
- int-abs/lels-01