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Theorem scolsorted-samecount-above-clean0
#r mx = #r mx0, #c mx = #c mx0, c < #c mx, scolsorted(mx, #c mx, mx0) ⊦ count(mx0[c]c, #clean0rows(mx0, i), #r mx, λ j. j < i) = count(mx[c]c, #clean0rows(mx0, i), #r mx, λ j. j < i)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
max0column-countcol
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 13
Proof steps: 25
Used lemmas:
scolsorted-clean0notls
,
clean0rows-allls
,
clean0rows-bounded
,
scolsorted-permcol
,
Used spec theorems:
filter-count
/oarray-sort/
perm-count
filter-count
/oarray-sort/
count-def
filter-count
/oarray-sort/
count-append-ind
filter-count
/oarray-sort/
fullcount-range
filter-count
/oarray-sort/
count-zero
Used simplifier rules:
nat-basic
/
f
nat-basic
/
lf-01
nat
/
lez
matrix+array
/
selcol-size
nat
/
ler
nat
/
le-def
nat
/
fle
matrix+array
/
selcol-get
matrix+array
/
selrow-get
matrix+array
/
selrow-size
nat
/
sub-base
nat-basic
/
lf-02
nat
/
fle-01
nat-basic
/
ls-02
nat-basic
/
eq-01
nat-basic
/
a
nat-basic
/
c
nat
/
let
nat
/
lels