Nuprl Lemma : pgeo-lpsep_wf
∀[p:ProjGeomPrimitives]. ∀[a:Line]. ∀[b:Point]. (a ≠ b ∈ ℙ)
Proof
Definitions occuring in Statement :
pgeo-lpsep: a ≠ b,
pgeo-primitives: ProjGeomPrimitives,
pgeo-line: Line,
pgeo-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
pgeo-lpsep: a ≠ b
Lemmas referenced :
pgeo-plsep_wf,
pgeo-point_wf,
pgeo-line_wf,
pgeo-primitives_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[p:ProjGeomPrimitives]. \mforall{}[a:Line]. \mforall{}[b:Point]. (a \mneq{} b \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-00_24_59
Last ObjectModification:
2017_10_17-PM-04_37_56
Theory : euclidean!plane!geometry
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