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Theorem mod-rec-neg
⊦ i < ~ j ∧ 0 < j → i |%| j = (i + j) |%| j
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
mod-rec-any
,
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:
mod-mult-01
,
mod-neg-def
,
Used spec theorems:
int-mult
/
numsucc
int-div
/
modex
int-mult
/
numeq-01
int-div
/
mod-mult-neg-03
int-div
/
mod-zero-05
Used simplifier rules:
int-abs
/
neg-07
int-div
/
div-elim-negpos
int-basic2
/
add-less
int-basic2
/
ls
int-basic2
/
lst-04
int-abs
/
zero-gels-04
int-abs
/
forward-le-04
int-abs
/
forward-lels
int-abs
/
forward-le-05
int-mult
/
eq-dist
int-mult
/
one
oelem
/intlista/
lel
int-div
/
mod-ngez
int-mult
/
Mult-zero
int-basic2
/
add-zero
int-basic1
/
ls-01
int-abs
/
lsone
int-abs
/
sub-ls
int-mult
/
zero-ls
int-abs
/
succ-02
int-mult
/
zero-gr-add
int-abs
/
sub-le-01
int-abs
/
succ-01
int-abs
/
lenls
int-mult
/
modzero-02
int-mult
/
ls-dist-03
int-mult
/
commutativity
int-mult
/
associativity
int-abs
/
numls-03
int-mult
/
ls-same
int-basic2
/
ls-01
int-basic2
/
add-in
int-div
/
mod-less-01
int-abs
/
forward-le-02
oelem
/intlista/
transitivity
int-abs
/
zero-gels-03
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
zero-gels-01
int-abs
/
mone-05
int-abs
/
numle-03
int-abs
/
abs-08
int-abs
/
neg-13
int-abs
/
lels
int-abs
/
lels-03