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Theorem scolsorted-count-below-clean0rows
#r mx = #r mx0, #c mx = #c mx0, c < #c mx, scolsorted(mx, #c mx, mx0) ⊦ count(mx[c]c, 0, #clean0rows(mx0, i), λ j. j < i) = #clean0rows(mx0, 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: 5
Proof steps: 10
Used lemmas:
count0-leq-clean0
,
scolsorted-colordered
,
sortedperm-count-splits
,
clean0rows-bounded
,
scolsorted-clean0notls
,
Used spec theorems:
filter-count
/oarray-sort/
count-size-ind
filter-count
/oarray-sort/
count-bounded-ind
Used simplifier rules:
nat-basic
/
f
nat-basic
/
lf-01
nat
/
lels
matrix+array
/
selcol-size
nat
/
le-def
nat-basic
/
lf-02
nat
/
fle
matrix+array
/
selcol-get
nat
/
lez
nat-basic
/
neq-01
nat
/
sub-base
list-perm
/oarray-sort/
ref
nat
/
fle-01
nat
/
ls-le-simp
nat-basic
/
refl-nat