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Theorem oc-put-toArc-rec
⊦ m < #r mx ∧ n < #c mx ∧ c ≤ #c mx → #oc(i, toArc(mx[m, n, j], c)) = #oc(i, toArc(mx, c)) + (i = j ∧ n < c ⊃ 1;0) - (mx[m, n] = i ∧ n < c ⊃ 1;0)
Type: A user defined theorem
Validity: The proof is valid.
Features: ls,
Comment:
Used by:
oc-put-toArc
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 14
Proof steps: 29
Used lemmas:
oc-toArc-positive
,
getcol-putsame
,
put-selcol
,
toArc-rec
,
toArc-base
,
Used spec theorems:
list-perm
/list-as-arrayinstance/
ocs-put-01
list-perm
/list-as-arrayinstance/
ocs-put-02
list-perm
/list-as-arrayinstance/
ocs-put
nat
/
prop-05
list-del
/list-as-arrayinstance/
in-get
Used simplifier rules:
list-perm
/list-as-arrayinstance/
oc-e
nat-basic
/
a
nat-basic
/
c
nat-basic
/
less-zero
nat-basic
/
f
nat
/
succ-01
nat-basic
/
succ
nat-basic
/
s-04
list
/list-as-arrayinstance/
a
list-perm
/list-as-arrayinstance/
ocappend
nat-basic
/
refl-nat
nat
/
lels-03
nat
/
sub-base
nat-basic
/
add-base
matrix+array
/
selcol-get
nat-basic
/
eq-01
matrix+array
/
selcol-size
nat
/
eq-01
matrix
/
put-same-content
nat
/
pred-03
nat-basic
/
z-01
list-perm
/list-as-arrayinstance/
oc-zero
list-perm
/list-as-arrayinstance/
notin
nat
/
elim-pred-c
nat-basic
/
oz
nat
/
add-01
nat
/
le-def
nat-basic
/
one-01
nat
/
eq-02
nat-basic
/
eq-02
nat-basic
/
trans-nat
nat-basic
/
lf
nat-basic
/
ls-02
nat-basic
/
neq-01