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Theorem exin2pot
⊦ 0 < j → (∃ i. 0 ≤ i ∧ 2 ^ i ≤ j ∧ j < 2 ^ (i + 1))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
exin2pot-neg
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 13
Proof steps: 25
Used lemmas:
pot-dist-pos
,
pot2-pos
,
Pot-pos
,
two-leone
,
Used spec theorems:
int-div
/
div2-nle-01
int-abs
/
le-def
int-mult
/
modlep-02
int-mult
/
modlep
Used simplifier rules:
intnat
/
labs
int-abs
/
abs-16
int-div
/
abs
int-div
/
div2-nle
int-basic1
/
lst-01
int-abs
/
lsone
int-abs
/
lels-02
int-div
/
div-elim-pos
int-mult
/
zero-ge-add
int-basic1
/
lf-01
int-mult
/
ls-same-01
int-abs
/
forward-lels
int-abs
/
forward-lsle
int-mult
/
one
int-mult
/
numls-09
int-basic2
/
pred
int-abs
/
mone-06
int-abs
/
numls-02
int-abs
/
zero-gs
int-abs
/
anti
int-basic1
/
lf-02
int-mult
/
mods-ls-04
int-abs
/
lels-04
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
absle
int-basic1
/
ls-01
int-mult
/
zero-gr
int-abs
/
forward-le-05
int-basic1
/
forward-pos
int-abs
/
forward-le-01
int-abs
/
lels
int-div
/
nummult-ls-02
int-abs
/
zero-gels-04
int-mult
/
commutativity
int-abs
/
lels-03
int-mult
/
associativity
int-abs
/
lels-01
int-abs
/
lenls