Nuprl Lemma : not-lsep-iff-colinear
∀g:EuclideanPlane. ∀a,b,c:Point. (¬a # bc ⇐⇒ Colinear(a;b;c))
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-lsep: a # bc,
geo-colinear: Colinear(a;b;c),
geo-point: Point,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A
Definitions unfolded in proof :
cand: A c∧ B,
and: P ∧ Q,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
euclidean-plane_wf,
euclidean-plane-axioms
Rules used in proof :
productElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
hypothesis,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b,c:Point. (\mneg{}a \# bc \mLeftarrow{}{}\mRightarrow{} Colinear(a;b;c))
Date html generated:
2017_10_02-PM-03_29_21
Last ObjectModification:
2017_08_07-AM-10_45_42
Theory : euclidean!plane!geometry
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