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Theorem ls-even-01
⊦ i % 2 = 0 ∧ j % 2 = 0 → (i / 2 < j / 2 ↔ i < j)
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
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: 19
Used lemmas:
two-even
,
lstwozero
,
div-elim
,
div-elim-negpos
,
Div-left
,
mod-neg-01
,
mult-div-switch
,
num-ls
,
ls-even
,
Used spec theorems:
Used simplifier rules:
int-abs
/
zero-gels-01
int-abs
/
forward-le-02
int-abs
/
le-def
int-mult
/
commutativity
int-mult
/
associativity
int-abs
/
neg-07
int-mult
/
minus-left
int-basic2
/
add-c
int-basic2
/
add-a
int-basic2
/
add-zero-rev
int-abs
/
negle-07
int-abs
/
neg-10
int-abs
/
forward-lels
int-abs
/
lels
int-abs
/
lels-03
int-basic2
/
ls-zero
int-abs
/
neg-13
int-abs
/
zero-gels-03
int-abs
/
neg-01
int-basic1
/
ls-01
int-abs
/
anti
int-basic1
/
irref
int-basic2
/
succ-01
int-basic1
/
trans
int-basic1
/
lf-01
int-abs
/
forward-le-05
int-mult
/
zero-ls
int-mult
/
zero-gr
int-abs
/
forward-lsle