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Theorem rowperms-clean1unchanged
#r mx = #r mx0, #c mx = #c mx0, #c mx ≠ 0, ∀ r. r < #r mx → perm(mx0[r]r, mx[r]r) ⊦ #clean1rows(mx0, i) = #clean1rows(mx, i) ↔ true
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment: sorting rows leaves the number of clean1 rows for i unchanged
Used by:
rowperms-dirtyrowsunchanged
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 11
Proof steps: 23
Used lemmas:
clean1rows-allge
,
clean1rows-notallge
,
clean1rows-bounded
,
Used spec theorems:
filter-count
/oarray-sort/
perm-count
list-perm
/oarray-sort/
sym
Used simplifier rules:
nat-basic
/
f
nat-basic
/
lf-01
nat
/
fle
nat
/
lels
nat-basic
/
c
nat-basic
/
a
nat-basic
/
eq-01
nat
/
eq-02
nat
/
ls-le-simp
nat
/
succ-01
nat
/
elim-sub
nat-basic
/
l-02
nat-basic
/
s-04
nat
/
lep
nat
/
let
nat-basic
/
ls-02
nat-basic
/
neq-04
nat-basic
/
l
nat
/
le-def
nat
/
lep-02
nat-basic
/
neq-01