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Theorem getarray-union-03

⊦ r -- _length ∈ st ∧ 0 ≤ i ∧ j ≤ st[r -- _length] .intval - i ∧ (∀ i1. i ≤ i1 ∧ i1 < i + j → r -- i1 ' ∈ st) → getarray(r, i, j, st0 ∪ st) = getarray(r, i, j, st)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: getarray-union-02,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 6
Proof steps: 12
Used lemmas: getArray-zero, get-rec-01,
Used spec theorems:
- storefunsx/union-at-right
Used simplifier rules:
- int-basic1/ls-01
- int-basic1/forward-pos
- int-basic2/add-less
- oelem/intlista/transitivity
- int-abs/forward-lsle
- int-abs/Sub-def
- int-abs/succ-01
- int-abs/lels-04
- int-abs/sub-add-06
- int-abs/sub-add-01
- int-abs/sub-le
- int-abs/numleledel-01
- int-abs/numle-02
- intnat/abs-pred
- ostore/javastore/notempty
- set-basic/javastore/ne-01
- oelem/intlista/irreflexivity
- int-abs/lep-01
- int-abs/lels-03
- storefunsx/union-at-right-01
- list/javavalues/app-01
- list/javavalues/a
- ostore/javastore/inkeys-01
- int-abs/forward-le-05
- storefuns/instore-01
- int-abs/forward-le-01
- int-abs/lels
- int-abs/lels-01
- int-basic2/add-c
- int-basic2/add-a
- int-abs/sub-le-01