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Theorem addarrays-at-other-01

⊦ r ∈ st ∧ posints(ints) → (addarrays(newref_list(i→n(countrefs(ints)), st), ty, ints, i, st)[r -- sk]) = st[r -- sk]

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 10
Proof steps: 22
Used lemmas: countrefs-i2n-02, getdims-zeroin, countrefs-getdims, getdims-empty, countdims-empty, countrefs-rec, countdims-rec, countrefs-one, getdims-zero, countdims-zero, countrefs-zero, getdims-rec, getdims-posints-01, getdims-empty-01, multi-at-other, countrefs-abs, addarrays-def, addarrays-empty, countrefs-empty, addarrays-at-other,
Used spec theorems:
- list-last/intlista/bc
Used simplifier rules:
- int-basic2/add-in
- int-basic2/add-c
- int-basic2/add-a
- int-mult/associativity
- int-mult/commutativity
- int-basic1/ls-01
- list/intlista/in-17
- list/intlista/in-append
- nat-basic2/one
- list/intlista/len
- list/intlista/len-02
- nat/ax-02
- nat-basic1/one
- nat-basic2/oz
- nat-basic2/a
- nat-basic2/c
- nat-basic2/one-03
- list-data/intlista/l
- int-abs/ax-02
- int-abs/lels-02
- int-abs/forward-le-05
- oelem/intlista/irreflexivity
- list/intlista/c-08
- list/intlista/c-07
- int-abs/lels
- int-abs/anti
- list/intlista/rest
- list/intlista/app
- list-last/intlista/b
- list/intlista/in-empty
- list/intlista/first
- int-abs/lels-04
- list/intlista/e
- list/intlista/app-02-ant
- int-abs/zero-gels-01
- int-abs/forward-lsle
- int-abs/forward-le-01
- valuesfuns/posints-rec
- list/intlista/a
- list/intlista/e-01
- list/intlista/c
- list-data/intlista/elim-list-c
- intnat/ini2-abs
- int-abs/forward-le-02
- valuesfuns/posints-empty
- storefuns/newrefs-one-01
- int-abs/lels-01
- intnat/abs-eq
- storefuns/newrefs-length
- storefuns/newrefs-in