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Theorem ls-mult-2pot
⊦ 0 < j ∧ 0 ≤ i ∧ 0 ≤ i0 → (j * 2 ^ i < 2 ^ i0 ↔ j < 2 ^ (i0 - i))
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
div-div-rec
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 4
Proof steps: 9
Used lemmas:
ls-2pot-01
,
pot2-pos
,
two-le
,
ls-pos-2pot
,
two-minus
,
pot-dist-pos
,
Used spec theorems:
int-abs
/
forward-lsle
int-mult
/
ls-same-04
Used simplifier rules:
int-abs
/
forward-le-05
int-abs
/
elim-sub
int-abs
/
forward-le-01
int-mult
/
associativity
int-mult
/
commutativity
int-abs
/
zero-gels-01
int-basic2
/
succ-01
int-abs
/
forward-le-02
int-abs
/
forward-lsle
int-basic1
/
trans
int-basic1
/
lf-01
int-abs
/
lels-01
int-basic2
/
ls-02
int-basic1
/
ls-01
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
zero-gels-03
int-abs
/
lep-01
int-abs
/
lels
int-abs
/
zero-gels-04
int-basic2
/
num-between