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Theorem int-ls-floor
⊦ i < ⌊r⌋ ↔ i.r + 1.r ≤ r
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
floor-le-int
,
negint-ls-floor
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 12
Used lemmas:
floor-gr-subone
,
floor-le
,
Used spec theorems:
real-abs
/
forward-lels
real-basic
/
eqint-add
real-basic
/
ls-num
int-abs
/
succ-02
Used simplifier rules:
real-abs
/
le-def
int-abs
/
lels-03
int-abs
/
lels
real-basic
/
less-add-cancel-l
real-basic
/
ls-num
int-abs
/
lenls
real-basic
/
add-assoc
real-basic
/
add-comm