Nuprl Lemma : eu-le-pt_wf
∀[e:EuclideanStructure]. ∀[a,b,c,d:Point]. (eu-le-pt(e;a;b;c;d) ∈ ℙ)
Proof
Definitions occuring in Statement :
eu-le-pt: eu-le-pt(e;a;b;c;d),
eu-point: Point,
euclidean-structure: EuclideanStructure,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eu-le-pt: eu-le-pt(e;a;b;c;d),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
euclidean-structure_wf,
eu-congruent_wf,
eu-between-eq_wf,
and_wf,
eu-point_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[e:EuclideanStructure]. \mforall{}[a,b,c,d:Point]. (eu-le-pt(e;a;b;c;d) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-06_43_28
Last ObjectModification:
2016_02_19-PM-02_31_38
Theory : euclidean!geometry
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