Nuprl Lemma : lsep-all-sym2
∀g:EuclideanPlane. ∀a,b,c:Point.  (a leftof bc 
⇒ {a # bc ∧ b # ca ∧ c # ab ∧ a # cb ∧ b # ac ∧ c # ba})
Proof
Definitions occuring in Statement : 
euclidean-plane: EuclideanPlane
, 
geo-lsep: a # bc
, 
geo-left: a leftof bc
, 
geo-point: Point
, 
guard: {T}
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
and: P ∧ Q
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
implies: P 
⇒ Q
, 
geo-lsep: a # bc
, 
or: P ∨ Q
, 
prop: ℙ
, 
uall: ∀[x:A]. B[x]
, 
subtype_rel: A ⊆r B
, 
guard: {T}
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
uimplies: b supposing a
Lemmas referenced : 
lsep-all-sym, 
geo-left_wf, 
geo-point_wf, 
euclidean-plane-structure-subtype, 
euclidean-plane-subtype, 
subtype_rel_transitivity, 
euclidean-plane_wf, 
euclidean-plane-structure_wf, 
geo-primitives_wf
Rules used in proof : 
cut, 
introduction, 
extract_by_obid, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
hypothesis, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
hypothesisEquality, 
inlFormation, 
isectElimination, 
applyEquality, 
because_Cache, 
sqequalRule, 
independent_functionElimination, 
productElimination, 
independent_pairFormation, 
instantiate, 
independent_isectElimination
Latex:
\mforall{}g:EuclideanPlane.  \mforall{}a,b,c:Point.
    (a  leftof  bc  {}\mRightarrow{}  \{a  \#  bc  \mwedge{}  b  \#  ca  \mwedge{}  c  \#  ab  \mwedge{}  a  \#  cb  \mwedge{}  b  \#  ac  \mwedge{}  c  \#  ba\})
Date html generated:
2018_05_22-AM-11_53_53
Last ObjectModification:
2018_03_26-PM-02_37_26
Theory : euclidean!plane!geometry
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