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Theorem square-nle
⊦ 0 ≤ j → ((j * (j + 1)) / 2 ≤ j ↔ j < 2)
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
square-nle-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 10
Proof steps: 16
Used lemmas:
div-elim-pospos
,
Used spec theorems:
int-mult
/
commutativity
int-abs
/
forward-lsle
int-mult
/
ls-pos
Used simplifier rules:
int-abs
/
forward-le
int-abs
/
forward-lsle
int-abs
/
forward-le-01
int-abs
/
numleledel-01
int-abs
/
numle-02
int-mult
/
zero-ge
int-mult
/
zero-gr
int-basic1
/
numlslsdel
int-abs
/
anti
int-abs
/
numlelsdel
int-mult
/
two-ls
int-abs
/
numadd-01
int-mult
/
ls-forward
int-abs
/
int-simp-07
int-mult
/
ls-pos
int-abs
/
numls-02
int-abs
/
mone-06
int-abs
/
zero-gels-04
int-basic1
/
two-ls
int-basic1
/
lf-02
int-abs
/
bet-01
int-abs
/
lels
int-mult
/
square-even
int-basic2
/
add-zero-rev
int-mult
/
numle-10
int-abs
/
succ-01
int-basic1
/
irref
int-abs
/
forward-lels
int-abs
/
lels-01
int-abs
/
lstwo-01
int-abs
/
lels-02
int-mult
/
one-01
int-mult
/
associativity
int-mult
/
commutativity
int-abs
/
forward-le-05
int-basic1
/
forward-pos
int-basic1
/
lf-01
int-basic2
/
add-a
int-basic2
/
add-c