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Theorem scolsorted-clean1notls
#c mx ≠ 0, #r mx = #r mx0, #c mx = #c mx0 ⊦ scolsorted(mx, #c mx0, mx0) → ¬ #clean1rows(mx, i) < #clean1rows(mx0, i)
Type: A user defined theorem
Validity: The proof is valid.
Features: las,
Comment: sorting cols does not decrease clean1cols
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 14
Proof steps: 30
Used lemmas:
scolsorted-def
,
scolsorted-colordered
,
scolsorted-permcol
,
count1-leq-clean1
,
clean1rows-notallge
,
clean1rows-bounded
,
Used spec theorems:
filter-count
/oarray-sort/
count-zero
filter-count
/oarray-sort/
perm-count
olist-min-max
/oarray-sort/
ordered-count-splits
filter-count
/oarray-sort/
count-add-dis
filter-count
/oarray-sort/
count-def
filter-count
/oarray-sort/
count-true
nat
/
le-addex
nat-basic
/
addex
Used simplifier rules:
nat-basic
/
f
nat-basic
/
lf-01
nat
/
fle
nat
/
lels
nat-basic
/
c
nat-basic
/
a
nat
/
eq-02
nat
/
ls-le-simp
nat
/
succ-01
nat
/
elim-sub
nat-basic
/
l-02
nat-basic
/
s-04
matrix+array
/
selrow-size
matrix+array
/
selrow-get
nat
/
let
matrix+array
/
selcol-size
nat
/
le-def
nat-basic
/
lf-02
nat-basic
/
lf
nat-basic
/
trans-nat
nat-basic
/
ls-02
nat
/
ler
matrix+array
/
selcol-get
nat
/
fle-01
nat-basic
/
eqs
nat
/
eqle-one
nat
/
le-add