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Theorem multg-at-ref

r ≠ r0, ¬ r0 ∈ refs, i→n(countrefs2(ints)) ≤ # refs ⊦ (addarraymultlist(r, ty, st, refs, ints, ints0, i)[r0 -- sk]) = st[r0 -- sk]

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: 18
Proof steps: 45
Used lemmas: countrefs2-pos-01, countrefs2-not-mone, countrefs2-pos, countrefs2-02, addarraymultlist_zero, countrefs2-empty, intssize-rec, addarraymultlist_more_1, countrefs2-03, countrefs2-01, addarraymultlist_more_2, addarraymultlist_more_0, addarraymultlist_one_not_0, addarraymultlist_one_0,
Used spec theorems:
Used simplifier rules:
- nat-basic2/l
- list-del/references/rest-in-01
- intnat/ini2-abs
- nat/ls-02
- list-del/references/rest-len
- nat/lels-01
- nat/le-one
- intnat/abs-zero
- int-mult/zero-eq
- intnat/labs-01
- int-abs/abs-04
- int-mult/abs-eqall
- int-abs/abs-16
- int-mult/le-abs
- int-abs/numadd-01
- int-abs/lep-01
- intnat/abs-succ-03
- nat-basic2/z-01
- int-abs/numleledel-01
- int-abs/leone
- int-abs/mone-06
- int-abs/numls-02
- int-abs/elim-sub
- list-data/references/size-01
- int-basic1/numlsf
- list/references/in-empty
- int-abs/numle-02
- int-mult/zero-ge
- intnat/num-i2n-le
- int-mult/zero-le
- int-abs/numle-03
- int-abs/mone-05
- int-mult/succ-rmerge
- int-abs/forward-le-01
- nat/lez
- list-data/intlista/size-01
- nat/lep-01
- list/references/in-06
- nat/lels
- nat-basic2/s
- list/references/len-02
- list/references/len
- list/references/a
- list/references/e-01
- list/references/c
- list-data/references/elim-list-c
- list/intlista/c-07
- intnat/n2i-add
- nat-basic2/oz
- nat-basic2/one-03
- list/intlista/c-08
- list-data/references/l
- nat-basic1/f
- nat/succ-01
- int-basic2/add-c
- int-basic2/add-a
- int-mult/commutativity
- int-mult/associativity
- int-mult/one
- nat-basic2/c
- nat-basic2/a
- nat-basic2/one
- list/intlista/len-02
- list/intlista/len
- list/intlista/a
- list/intlista/e-01
- list/intlista/c
- list-data/intlista/elim-list-c
- int-abs/forward-le-05
- int-basic1/two-ls
- int-abs/ax-01
- list-data/intlista/l
- nat-basic1/one
- nat/ax-02
- int-abs/lels-03
- int-abs/lels
- int-abs/ax-02
- addarray/lookup-1dim
- int-abs/lels-01
- javastore/look-ins