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Theorem mod-ls-same-02
j ≠ 0 ⊦ i < i % j ↔ i < 0 ∧ (abs(j) = 1 ∨ abs(j) ≤ abs(i))
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
div-add-nosucc-neg
,
div-add1-negpos-neg-01
,
div-add1-negpos-neg-02
,
div-minus-onediff-01
,
div-minus255-256-01
,
exeven
,
ls-even-01
,
mod-grz-01
,
mod-nls-03
,
modeven-neg
,
modex
,
modmod-add-case
,
modmod-add-if
,
modmod-add2-posneg-neg-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 7
Proof steps: 20
Used lemmas:
div-elim-pospos
,
div-elim-posneg
,
mod-nls-01
,
div-elim-negpos
,
div-elim-negneg
,
mod-zero-05
,
Used spec theorems:
int-abs
/
le-def
int-abs
/
neg-13
Used simplifier rules:
int-abs
/
absls-01
int-abs
/
abs-16
int-abs
/
lels-02
int-abs
/
neg-13
int-abs
/
lep
int-mult
/
zero-ge
int-abs
/
anti
int-basic2
/
ls-01
int-basic1
/
irref
int-abs
/
zero-gels-04
int-abs
/
forward-lele
int-mult
/
succ-rmerge
int-mult
/
pred-rmerge
int-abs
/
numadd-01
int-abs
/
negeq
int-abs
/
numls-02
int-abs
/
mone-06
int-mult
/
zero-gr-add-01
int-abs
/
numle-02
int-abs
/
mone-08
int-abs
/
forward-le-04
int-mult
/
Mult-zero
int-basic2
/
add-zero
int-mult
/
one
int-abs
/
zero-gels-03
int-mult
/
minus-one-01
int-abs
/
neg-15
int-abs
/
minus-add
int-abs
/
sub-le
int-abs
/
lels-03
int-abs
/
elim-sub
int-abs
/
forward-le-01
int-abs
/
forward-lels
int-abs
/
lels
int-abs
/
zero-gels-01
int-abs
/
forward-le-02
int-abs
/
forward-lsle
int-abs
/
zero-gels
int-abs
/
abs-08
int-abs
/
neg-07
int-mult
/
zero-ls-01
int-abs
/
forward-le-05
int-basic1
/
ls-01
int-basic1
/
lst-01
int-basic2
/
ls
int-mult
/
zero-ls
int-abs
/
lels-04
int-mult
/
associativity
int-mult
/
commutativity
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
lels-01