Nuprl Lemma : pgeo-plsep_wf
∀[p:ProjGeomPrimitives]. ∀[a:Point]. ∀[b:Line]. (a ≠ b ∈ ℙ)
Proof
Definitions occuring in Statement :
pgeo-plsep: 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-primitives: ProjGeomPrimitives,
pgeo-line: Line,
pgeo-point: Point,
pgeo-plsep: a ≠ b,
record+: record+,
record-select: r.x,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
guard: {T},
prop: ℙ
Lemmas referenced :
subtype_rel_self,
pgeo-line_wf,
pgeo-point_wf,
pgeo-primitives_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
dependentIntersectionElimination,
dependentIntersectionEqElimination,
thin,
hypothesis,
applyEquality,
tokenEquality,
instantiate,
extract_by_obid,
isectElimination,
universeEquality,
functionEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
cumulativity,
hypothesisEquality,
axiomEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[p:ProjGeomPrimitives]. \mforall{}[a:Point]. \mforall{}[b:Line]. (a \mneq{} b \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-00_23_20
Last ObjectModification:
2017_10_31-PM-01_53_52
Theory : euclidean!plane!geometry
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