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Theorem scolsorted-clean0notls
#c mx ≠ 0, #r mx = #r mx0, #c mx = #c mx0 ⊦ scolsorted(mx, #c mx0, mx0) → ¬ #clean0rows(mx, i) < #clean0rows(mx0, i)
Type: A user defined theorem
Validity: The proof is valid.
Features: las,
Comment: sorting cols does not decrease clean0cols
Used by:
max0column-clean0rowsbounded
,
scolsorted-count-below-clean0rows
,
scolsorted-samecount-above-clean0
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 14
Proof steps: 28
Used lemmas:
count0-leq-clean0
,
sortedperm-count-splits
,
scolsorted-def
,
count0-leq-clean0-ind
,
clean0rows-notallls
,
clean0rows-bounded
,
Used spec theorems:
filter-count
/oarray-sort/
count-zero
filter-count
/oarray-sort/
count-size-ind
list-perm
/oarray-sort/
in
list-del
/oarray-sort/
in-get
Used simplifier rules:
nat-basic
/
f
nat-basic
/
lf-01
nat
/
fle
nat
/
lels
matrix+array
/
selrow-get
matrix+array
/
selrow-size
nat-basic
/
lf-02
nat
/
lels-03
matrix+array
/
selcol-size
nat-basic
/
refl-nat
matrix+array
/
selcol-get
nat
/
le-def
nat-basic
/
lf
nat-basic
/
trans-nat
nat-basic
/
ls-02
nat
/
ler
nat
/
fle-01
nat
/
let
nat
/
ls-le-simp