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Theorem square-ex
⊦ 0 < i → (∃ j. 0 < j ∧ j * j ≤ i ∧ i < (j + 1) * (j + 1))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
int-square
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 17
Used lemmas:
one-01
,
le-pos
,
zero-gr
,
square-le
,
le-one
,
numle-03
,
le-dist-02
,
one
,
dist-lsplit
,
commutativity
,
associativity
,
square-ls
,
Used spec theorems:
Used simplifier rules:
int-abs
/
forward-le-01
int-basic2
/
succ-01
int-abs
/
zero-gels-04
int-abs
/
mone-06
int-abs
/
numls-02
int-abs
/
int-add-pos
int-abs
/
le-add-03
int-abs
/
numle-01
int-basic2
/
zero-02
int-abs
/
numadd
int-basic2
/
add-zero-rev
int-abs
/
lep-02
int-abs
/
numle-03
int-abs
/
zero-gels-02
int-basic1
/
trans
int-basic1
/
lf-01
int-abs
/
forward-lels
int-abs
/
forward-le-05
int-abs
/
sub-ls
int-abs
/
succ-01
int-abs
/
sub-le-01
int-abs
/
les
int-abs
/
numlelsdel-01
int-abs
/
ler
int-abs
/
succ-02
int-abs
/
lep
int-abs
/
abs-16
int-abs
/
abs-17
int-abs
/
forward-lele
int-abs
/
anti
int-basic1
/
ls-01
int-abs
/
lels-01
int-abs
/
sub-pred
int-abs
/
sub-ls-01
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
Sub-def
int-abs
/
lels
int-abs
/
bet
int-basic1
/
forward-pos
int-basic1
/
lf-02