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Theorem square-interval
(i * (i + 1)) / 2 ≤ (j * (j + 1)) / 2 + j0, (j * (j + 1)) / 2 + j0 < ((i + 1) * (i + 2)) / 2, j0 ≤ j, 0 ≤ i, 0 ≤ j0 ⊦ i = j
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: 10
Proof steps: 12
Used lemmas:
square-even-01
,
div-lezero
,
mult-ls-01
,
square-even
,
square-even-02
,
div2zero
,
square-ls-01
,
Used spec theorems:
int-mult
/
square-interval
int-mult
/
dist-rsplit
Used simplifier rules:
int-abs
/
ler
int-abs
/
succ-02
int-abs
/
forward-le-01
int-mult
/
ls-pos
int-abs
/
lels-03
int-abs
/
lels
int-mult
/
square-zero-01
int-basic2
/
add-zero-rev
int-mult
/
le-pos-01
int-abs
/
forward-le-05
int-abs
/
lsone
int-abs
/
anti
int-abs
/
zero-gels-01
int-basic1
/
lf-01
int-basic1
/
trans
int-basic1
/
lf-02
int-abs
/
forward-lsle
int-abs
/
forward-le-02
int-abs
/
forward-lels
int-abs
/
forward-le-04
int-abs
/
forward-lele
int-basic2
/
succ-01
int-mult
/
ls-dist-03
int-abs
/
numls-03
int-mult
/
numls-03
int-mult
/
one
int-abs
/
lep-01
int-mult
/
square-ls-04
int-basic1
/
lst-01
int-abs
/
lenls
int-basic2
/
add-a
int-basic2
/
add-c
int-mult
/
associativity
int-mult
/
zero-gr-02
int-abs
/
numls-02
int-abs
/
mone-06
int-abs
/
lels-02
int-abs
/
lels-01
int-mult
/
zero-gr
int-basic2
/
zero-02
int-mult
/
commutativity