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Theorem scolsort-dirtyboundhalf
#r mx0 = #r mx, #c mx0 = #c mx, #c mx ≠ 0 ⊦ scolsorted(mx, #c mx, mx0) ∧ mx0.dirtyrows≤(bound) ∧ srowsorted(mx0, #r mx0, mx0) → mx.dirtyrows≤(bound /↑ 2)
Type: A user defined theorem
Validity: The proof is valid.
Features: ls,
Comment:
Used by:
shearsort-correct
,
sortcols-correct
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 29
Proof steps: 64
Used lemmas:
countodd-maxcol0-bounded
,
countevn-maxcol0-bounded
,
clean0rows-bounded
,
count-add-even-odd-ind
,
max0column-countcol
,
divup-def
,
scolsorted-def
,
max0column-determines-clean1rows
,
max0column-clean0rowsbounded
,
exists-max0column
,
dirtyrows-def
,
dirtyrowsbound-def
,
Used spec theorems:
nat-mult
/
eq
nat
/
le-addex
nat-even
/
Min-left
Used simplifier rules:
nat-basic
/
f
nat
/
le-def
nat-basic
/
lf-01
nat
/
ls-le-simp
nat
/
ge
nat-basic
/
refl-nat
nat
/
ler
nat-basic
/
c
nat-basic
/
a
nat-basic
/
eqs
nat
/
fle
nat-mult
/
mult-c
nat-mult
/
mult-a
nat-div
/
two-mdiv2-02
nat-mult
/
le-num
nat
/
anti
nat-div
/
le-div-to-mult
nat
/
lels
nat-basic
/
s-04
nat-basic
/
l
nat-div
/
ls-02
nat-div
/
two-zero-01-01
nat
/
le-ls-simp
nat
/
fle-01
nat-div
/
div-elim
nat-basic
/
lf-02
nat
/
lels-02
nat
/
l-num-05
nat-basic
/
one-01
nat-basic
/
succ
nat-basic
/
add-base
nat-mult
/
two-succ-05
nat
/
let
nat-basic
/
l-02
nat-mult
/
zero-02
nat-mult
/
two-ls-01
nat-basic
/
lf
nat-basic
/
trans-nat
nat-basic
/
l-05
matrix+array
/
selcol-size
nat-basic
/
eq-01
nat-even
/
Min-right
nat-even
/
min-a
nat-even
/
min-c