Nuprl Lemma : eu-between-same
∀[e:EuclideanPlane]. ∀[a,b:Point]. (¬a-b-a)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
eu-between: a-b-c,
eu-point: Point,
uall: ∀[x:A]. B[x],
not: ¬A
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
euclidean-plane: EuclideanPlane,
euclidean-axioms: euclidean-axioms(e),
and: P ∧ Q,
prop: ℙ,
guard: {T}
Lemmas referenced :
eu-between_wf,
eu-point_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
setElimination,
rename,
productElimination,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
independent_functionElimination,
voidElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
because_Cache,
isect_memberEquality
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[a,b:Point]. (\mneg{}a-b-a)
Date html generated:
2016_05_18-AM-06_34_12
Last ObjectModification:
2015_12_28-AM-09_28_00
Theory : euclidean!geometry
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