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Theorem fac-le
⊦ 0 < i ∧ 0 < j → (fac(i) ≤ fac(j) ↔ i ≤ j)
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 18
Used lemmas:
fac-not-neg
,
fac-le-zero
,
fac-one
,
fac-le-one
,
fac-zero
,
fac-rec
,
Used spec theorems:
int-mult
/
le-one
int-mult
/
pnle-pos
int-mult
/
pnls-pos
Used simplifier rules:
int-abs
/
elim-sub
int-abs
/
succ-01
int-abs
/
forward-le-01
int-abs
/
mone-06
int-abs
/
numls-02
int-abs
/
succ-02
intnat
/
rax-04
nat-basic2
/
s
intnat
/
labs
int-abs
/
absle
nat-basic2
/
a
nat-basic2
/
c
oelem
/intlista/
irreflexivity
int-abs
/
leone
int-abs
/
zero-gels-04
int-abs
/
lenls
int-abs
/
forward-lsle
oelem
/intlista/
lel
int-abs
/
anti
int-abs
/
numle-03
int-abs
/
mone-05
int-abs
/
lels
int-abs
/
bet
int-mult
/
associativity
int-mult
/
commutativity
int-abs
/
forward-le-05
int-basic2
/
zero-04
int-basic1
/
ls-01
int-abs
/
le-add
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
numle-02
int-abs
/
numleledel-01
int-abs
/
lels-01