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Theorem zero-ls-02
⊦ 0.r ≤ r → (r * r0 < 0.r ↔ r0 < 0.r ∧ r ≠ 0.r)
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
abs-eqall
,
abs-ls-same
,
abs-not-neg
,
mods-zero-07
,
square-abs
,
square-interval
,
square-lez
,
square-zero-01a
,
square-zero-02
,
twice-ls-zero
,
zero-ge-02
,
zero-ge-add-01
,
zero-ls-case
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 1
Proof steps: 2
Used lemmas:
mult-com
,
mult-ass
,
zero-ls
,
mult-zero
,
Used spec theorems:
Used simplifier rules:
real-abs
/
lels-02
real-abs
/
lels
real-abs
/
lels-03
real-abs
/
forward-lsle
real-abs
/
zero-gels-01
real-basic
/
ls-num