### Nuprl Lemma : eu-perp-in_wf

`∀[e:EuclideanPlane]. ∀[x,a,b,c,d:Point].  (Perp-in(x; ab; cd) ∈ ℙ)`

Proof

Definitions occuring in Statement :  eu-perp-in: `Perp-in(x; ab; cd)` 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-perp-in: `Perp-in(x; ab; cd)` prop: `ℙ` and: `P ∧ Q` euclidean-plane: `EuclideanPlane` so_lambda: `λ2x.t[x]` implies: `P `` Q` so_apply: `x[s]` all: `∀x:A. B[x]`
Lemmas referenced :  eu-colinear_wf all_wf eu-point_wf eu-perpendicular_wf euclidean-plane_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule productEquality lemma_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis because_Cache lambdaEquality functionEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality

Latex:
\mforall{}[e:EuclideanPlane].  \mforall{}[x,a,b,c,d:Point].    (Perp-in(x;  ab;  cd)  \mmember{}  \mBbbP{})

Date html generated: 2016_05_18-AM-06_43_17
Last ObjectModification: 2015_12_28-AM-09_22_35

Theory : euclidean!geometry

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