Nuprl Lemma : pgeo-psep_wf
∀[p:ProjGeomPrimitives]. ∀[a,b:Point]. (a ≠ b ∈ ℙ)
Proof
Definitions occuring in Statement :
pgeo-psep: a ≠ b,
pgeo-primitives: ProjGeomPrimitives,
pgeo-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
pgeo-psep: a ≠ b,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
pgeo-primitives_wf,
pgeo-point_wf,
pgeo-plsep_wf,
pgeo-incident_wf,
pgeo-line_wf,
exists_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
productEquality,
lambdaEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[p:ProjGeomPrimitives]. \mforall{}[a,b:Point]. (a \mneq{} b \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-00_24_23
Last ObjectModification:
2017_11_16-AM-10_31_46
Theory : euclidean!plane!geometry
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