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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