Nuprl Lemma : LP-sep-or
∀g:ProjectivePlaneStructure. ∀l:Line. ∀p:Point.  (l ≠ p 
⇒ (∀q:Point. (q ≠ l ∨ q ≠ p)))
Proof
Definitions occuring in Statement : 
projective-plane-structure: ProjectivePlaneStructure
, 
pgeo-lpsep: a ≠ b
, 
pgeo-psep: a ≠ b
, 
pgeo-plsep: a ≠ b
, 
pgeo-line: Line
, 
pgeo-point: Point
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
or: P ∨ Q
Definitions unfolded in proof : 
prop: ℙ
, 
subtype_rel: A ⊆r B
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
implies: P 
⇒ Q
, 
all: ∀x:A. B[x]
Lemmas referenced : 
projective-plane-structure_wf, 
pgeo-line_wf, 
projective-plane-structure_subtype, 
pgeo-point_wf, 
pgeo-lpsep_wf, 
pgeo-LPSepOr_wf
Rules used in proof : 
sqequalRule, 
because_Cache, 
applyEquality, 
isectElimination, 
hypothesis, 
dependent_set_memberEquality, 
hypothesisEquality, 
thin, 
dependent_functionElimination, 
sqequalHypSubstitution, 
extract_by_obid, 
cut, 
introduction, 
lambdaFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
\mforall{}g:ProjectivePlaneStructure.  \mforall{}l:Line.  \mforall{}p:Point.    (l  \mneq{}  p  {}\mRightarrow{}  (\mforall{}q:Point.  (q  \mneq{}  l  \mvee{}  q  \mneq{}  p)))
Date html generated:
2018_05_22-PM-00_29_49
Last ObjectModification:
2017_11_27-PM-04_19_25
Theory : euclidean!plane!geometry
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