Nuprl Lemma : eu-perpendicular_wf
∀[e:EuclideanPlane]. ∀[a,b,c:Point]. (Per(a;b;c) ∈ ℙ)
Proof
Definitions occuring in Statement :
eu-perpendicular: Per(a;b;c),
euclidean-plane: EuclideanPlane,
eu-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eu-perpendicular: Per(a;b;c),
euclidean-plane: EuclideanPlane,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
exists_wf,
eu-point_wf,
and_wf,
eu-midpoint_wf,
eu-congruent_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[a,b,c:Point]. (Per(a;b;c) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-06_42_30
Last ObjectModification:
2015_12_28-AM-09_22_22
Theory : euclidean!geometry
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