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Theorem mod-by6
⊦ 0 ≤ i → (i * (i + 1) * (2 * i + 1)) % 6 = 0
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 8
Proof steps: 16
Used lemmas:
mod-zero-num
,
mod-add1-pospos
,
modby6-help
,
Used spec theorems:
int-mult
/
zero-ls
Used simplifier rules:
int-abs
/
mone-08
int-abs
/
zero-gels-04
int-abs
/
zero-gels-01
int-basic2
/
succ-01
int-abs
/
forward-le-02
int-basic1
/
lf-02
int-basic1
/
trans
int-basic1
/
lf-01
int-abs
/
lels-02
int-mult
/
zero-ge-02
int-mult
/
square-gez
int-mult
/
zero-ge
int-basic2
/
zero-02
int-mult
/
modzero
int-mult
/
commutativity
int-basic1
/
ls-01
int-abs
/
lels-01
int-abs
/
forward-le-05
int-abs
/
leone
int-abs
/
sub-le-01
int-abs
/
Sub-def
int-abs
/
sub-pred
int-abs
/
elim-sub
int-abs
/
forward-le-01
int-abs
/
numleledel-01
int-abs
/
numle-02
int-abs
/
mone-06
int-abs
/
numls-02
int-mult
/
associativity
int-basic2
/
add-c
int-basic2
/
add-a