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Theorem addarrays-at-other

⊦ ¬ r ∈ refs ∧ # refs = i→n(countrefs(ints)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) → (addarrays(refs, 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: addarrays-at-other-01, addarrays-subset, nouninit-addarrays,
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: countrefs-i2n-02, getdims-zeroin, countrefs-i2n-01, 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,
Used spec theorems:
- list-last/intlista/bc
- intnat/num-n2i-eq
Used simplifier rules:
- int-abs/numle-02
- int-basic1/numlsf
- intnat/minus-one
- list-data/references/l
- int-mult/eq-one-neg
- int-abs/negeq
- int-mult/one-01
- int-basic1/ls-01
- list/intlista/in-17
- list/intlista/in-append
- int-basic2/add-c
- int-basic2/add-a
- int-mult/commutativity
- int-mult/associativity
- 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
- valuesfuns/posints-empty
- int-abs/forward-le-05
- oelem/intlista/irreflexivity
- list/intlista/c-08
- list/intlista/c-07
- int-abs/lels
- int-abs/anti
- intnat/num-n2i-eq
- list/intlista/rest
- list/intlista/app
- list-last/intlista/b
- list/intlista/in-empty
- list/intlista/first
- int-abs/lels-04
- int-abs/lels-01
- list/intlista/e
- list/intlista/app-02-ant
- intnat/n2n
- 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-01