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Theorem abs-pred
⊦ i→n(i - 1) < i→n(i) ↔ 0 < i
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
Used by units in proved state:
int-pot
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 3
Proof steps: 6
Used lemmas:
abs-neg
,
num-i2n-le-01
,
Int2nat-neg
,
Int2nat-pos
,
abs-zero
,
num-i2n-le-02
,
sub
,
Used spec theorems:
Used simplifier rules:
int-abs
/
forward-le-02
int-abs
/
lels-02
nat-basic1
/
f
int-abs
/
forward-le-04
nat-basic1
/
ref-1
nat-basic2
/
s
int-abs
/
lels-03
int-abs
/
lels
int-abs
/
leone
int-basic1
/
ls-01
int-basic1
/
lst-01
int-abs
/
neg-15
int-abs
/
minus-02
int-abs
/
sub-ls
int-abs
/
sub-ls-01
int-basic2
/
add-zero-rev
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
lsone
int-abs
/
zero-gels-03
int-abs
/
sub-sub
int-abs
/
num-subadd
int-abs
/
neg-06
nat-basic2
/
l-02
nat-basic2
/
a
nat-basic2
/
c
int-abs
/
lels-01
int-abs
/
zero-gels-01
int-abs
/
negle-13
int-abs
/
numle-02
int-abs
/
mone-08
nat
/
ls-01
nat-mult
/
two-02
nat-mult
/
ls2-03
nat-mult
/
mult-a
nat-mult
/
mult-c