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Theorem modmod-add-case
0 < j ⊦ (i + i0 % j) % j = (i + i0) % j ∨ (i + i0 % j) % j = (i + i0) % j + j ∨ (i + i0 % j) % j = (i + i0) % j - j
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
modmod-add-law-pos
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 18
Used lemmas:
modmod-add2-posneg-neg-02
,
modmod-add2-posneg-neg-01
,
mod-ls-same-02
,
modmod-add2-posneg-neg
,
modmod-add2-posneg-pos
,
modmod-add-zero
,
modmod-add2-negpos-pos-02
,
modmod-add2-negpos-pos-01
,
mod-zero-09
,
mod-one
,
mod-ls-same-01
,
modmod-add2-negpos-pos
,
modmod-add-02
,
modmod-add2-negpos-neg
,
modmod-add
,
Used spec theorems:
Used simplifier rules:
int-abs
/
forward-le-05
int-basic1
/
ls-01
int-abs
/
zero-gels-03
int-abs
/
sub-eq
int-basic2
/
eq
int-mult
/
add-mult-two
int-mult
/
zero-neq-01
int-mult
/
associativity
int-mult
/
commutativity
int-abs
/
Sub-def
int-basic2
/
succ-01
int-abs
/
forward-le-02
int-basic1
/
trans
int-basic1
/
lf-01
int-abs
/
lels-01
int-basic2
/
ls
int-abs
/
forward-lele
int-abs
/
forward-le-04
int-abs
/
forward-lels
int-abs
/
negle-07
int-abs
/
abs-08
int-abs
/
abs-16
int-abs
/
numls-03
int-basic2
/
add-zero-rev
int-basic2
/
ls-01
int-abs
/
forward-lsle
int-abs
/
forward-le-01
int-abs
/
zero-gels-04
int-abs
/
zero-gels-01
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
lels
int-abs
/
lels-03