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Theorem putarray-addarray-01

⊦ 0 ≤ i ∧ 0 ≤ j ∧ i ≤ j → putArray(vals, r, i, addarray(r, ty, j, st)) = (addarray (r, ty, mklist(initial_value(ty), i→n(i)) + vals + ((j - i + n→i(# vals) > 0 ⊃ mklist(initial_value(ty), i→n(j - i + n→i(# vals))); [])), st) [r -- _length, intval(j) ] )

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: 57
Proof steps: 139
Used lemmas: add-at-neg, in-1dim-other-index, in-1dim-05, in-1dim-14, in-1init-02, add-in-other, add-at-01, lookup-1init, lookup-1dim, add-at-04, at-field-1dim, in-1dim-fskey, type-1init, type-1dim, add-in, type-in, at-1dim-other-index, num-at-1dim, at-1dim, add-at-other-index, add-at-ok, in-1dim-16, in-1dim-other, in-1dim-01, in-add, add-in-fskey, in-init-01, length-1dim, length-1dim-02,
Used spec theorems:
- storearrays/putArray-at
- int-abs/numle-03
- nat-basic2/c
- intnat/num-i2n-eq
- int-abs/numle-02
- list-del/javavalues/get-append-grt
- intnat/num-i2n-le-02
- store/javastore/Extension
- storearrays/putar-in
- storekey/ex-04
- storearrays/putar-at
- storearrays/putar-atother
- list-del/javavalues/get-mklist-01
- list-del/javavalues/get-append-less
- intnat/add-01
- storearrays/putArray-in
Used simplifier rules:
- storearrays/putar-inref
- int-abs/forward-le
- storearrays/putarray-type
- refkey/sel-01
- refkey/sel-02
- specialkeys/type-03
- storefuns/instore-01
- list/javavalues/app
- storearrays/putarray-field
- nat-basic2/eq-01
- list-del/javavalues/get-append-less
- int-abs/abs-12
- int-abs/zero-gs
- int-abs/forward-lele
- nat/lels
- intnat/inni-le
- nat/lep
- nat/le-ls-simp
- int-abs/negle-13
- int-abs/neg-06
- intnat/le
- int-abs/le-add
- intnat/nat2int
- int-abs/sub-le-01
- intnat/labs-01
- nat/elim-sub
- intnat/nat2int-08
- int-basic2/add-less
- list-del/javavalues/get-append-grt
- intnat/labs
- int-abs/absle
- int-abs/abs-16
- storearrays/putArray-at-in
- int-abs/zero-gels-04
- storekey/test-06
- storekey/sel-06
- int-abs/zero-gels-01
- int-abs/lels-03
- int-abs/forward-lels
- oelem/intlista/transitivity
- int-abs/forward-lsle
- int-abs/forward-le-02
- intnat/num-n2i-ls-02
- nat-basic1/z
- list-data/javavalues/l
- int-abs/lels-04
- int-basic2/ls
- int-basic1/ls-01
- nat-basic2/c
- nat-basic2/a
- intnat/i2i-pos
- intnat/i2i-pos-01
- intnat/n2i-add
- list/javavalues/a
- list-last/javavalues/mk-len
- list/javavalues/len
- storekey/test-08
- specialkeys/len
- storekey/elim-04
- storekey/test-02
- storekey/test
- specialkeys/type-04
- specialkeys/type-06
- javavalue/inj-09
- storekey/test-01
- storearrays/putar-atref
- refkey/inj-01
- refkey/elim
- store/javastore/At-other
- storearrays/putArray-in
- storearrays/putarray-length
- store/javastore/At-same
- javavalue/inj-04
- store/javastore/In-insert
- int-abs/forward-le-05
- int-basic2/ls-02
- int-basic2/ls-01
- int-abs/lep
- int-abs/elim-sub
- int-abs/lels-01
- int-abs/forward-le-01
- int-abs/lels
- int-basic2/add-c
- int-basic2/add-a
- int-basic2/ax-04
- int-abs/sub-ls-01
- int-abs/ax-02