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Theorem square-interval
r * (r + 1.r) ≤ r0 * (r0 + 1.r) + 2.r * r2, r0 * (r0 + 1.r) + 2.r * r2 < (r + 1.r) * (r + 2.r), r2 ≤ r0, 0.r ≤ r, 0.r ≤ r2 ⊦ r < r0 + 1.r ∧ r0 < r + 1.r
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
square-interval-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 5
Proof steps: 10
Used lemmas:
zero-ls-02
,
le-posint
,
square-le-04
,
mult-com
,
mult-ass
,
mult-one
,
distr
,
Used spec theorems:
Used simplifier rules:
real-basic
/
add-comm
real-basic
/
add-assoc
real-basic
/
ls-02
real-basic
/
less-add-cancel-l
real-abs
/
forward-lele
real-abs
/
forward-lels
real-abs
/
lels
real-abs
/
lep-02
real-basic
/
ls-num
real-basic
/
ls
real-basic
/
lsnum-addboth1
real-abs
/
forward-lsle
real-basic
/
trans
real-abs
/
zero-gels-03
real-abs
/
le-def
int-basic2
/
add-c
int-basic2
/
add-a
real-basic
/
eqint-add
real-abs
/
lenls
real-abs
/
lep-01
real-abs
/
le-num