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Theorem multi-lengthin

⊦ r ∈ refs ∧ # refs = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → r -- _length ∈ addmultiarrays(refs, i, acc, ty, ints, st) ∧ is_integervalue(addmultiarrays(refs, i, acc, ty, ints, st)[r -- _length]) ∧ 0 ≤ (addmultiarrays(refs, i, acc, ty, ints, st)[r -- _length]) .intval

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: 15
Proof steps: 46
Used lemmas: countrefs-one, countrefs-zero, multi-at-other, multi-refin, countrefs-lastn-03, countrefs-lastn, countrefs-rec-02, countrefs-not-zero-01, countrefs-i2n, countrefs-rec-01, addmultiarrays-rec, addmultiarrays-done, addmultiarrays-base,
Used spec theorems:
- list-del/references/lastN-append-01
- list-del/references/lastn-firstn-in-01
- addarray/length-1dim-02
Used simplifier rules:
- addarray/length-1dim
- list/intlista/in-empty
- list-last/intlista/b
- valuesfuns/posints-empty
- list/intlista/app
- nat/le-ls-simp
- nat/eq-02
- nat-basic2/eq
- javavalue/elim-02
- nat/ls-le-simp
- list/references/in-01
- nat-basic2/s
- list-data/references/l
- nat-basic1/lf-01
- nat/eqle-one
- nat/lels-03
- nat/succ-01
- nat/anti
- nat-basic2/eq-inc-neq
- nat/lep-02
- oelem/intlista/irreflexivity
- list/intlista/c-08
- list/intlista/in-01
- list-last/intlista/bin
- valuesfuns/posints-rec-01
- int-abs/lels-04
- list/intlista/e
- list/intlista/app-02-ant
- list/references/in-06
- nat/lep
- nat-mult/coef-18
- nat/lep-01
- nat/lels
- nat-basic2/l
- list-del/references/first-length
- list/references/e-01
- nat-basic2/eq-01
- list/references/len
- list-data/references/size-01
- list-del/references/firstN-rec
- nat-basic2/eqs
- nat/lels-01
- nat-basic1/lf-02
- nat-basic1/f
- nat-basic2/l-02
- storefuns/instore-01
- oelem/intlista/transitivity
- int-abs/forward-lsle
- int-abs/forward-le-02
- int-abs/zero-gels-01
- nat/elim-sub
- list/references/in-append
- list/references/a
- list/references/in-14
- list-del/references/lastN-empty
- intnat/abs-zero
- list-data/references/elim-list-c
- int-mult/commutativity
- int-mult/associativity
- nat-mult/mult-c
- nat-mult/mult-a
- nat-mult/rsucc-02
- intnat/rax-04
- int-abs/mone-06
- int-abs/numls-02
- int-abs/succ-01
- int-abs/numadd-01
- int-abs/elim-sub
- list/references/c
- list/intlista/c-07
- int-abs/ax-02
- int-abs/lels
- int-basic1/ls-01
- nat-basic2/one-03
- nat/ax-02
- nat-basic1/one
- nat-basic2/oz
- intnat/n2i-add
- int-abs/numsub
- int-basic2/ax-04
- int-basic2/add-a
- int-basic2/add-c
- list/references/onein
- list/references/len-02
- list/references/in-17
- list/references/first
- addarray/length-init
- addarray/length-1init-01
- javavalue/test-25
- javavalue/sel-04
- intnat/nat2int-08
- int-abs/forward-le-05
- int-abs/lels-02
- list/intlista/in-06
- list-last/intlista/bapp
- nat-basic2/c
- nat-basic2/a
- list-data/intlista/l
- nat-basic2/one
- list/intlista/len-02
- list/intlista/len
- int-abs/zero-gels-04
- valuesfuns/posints-rec
- list/intlista/a
- list/intlista/e-01
- list/intlista/c
- list-data/intlista/elim-list-c
- int-abs/forward-le-01
- int-abs/lels-01