Nuprl Lemma : geo-plsep_wf
∀[e:GeometryPrimitives]. ∀[p:Point]. ∀[l:Line]. (p # l ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-plsep: p # l,
geo-line: Line,
geo-primitives: GeometryPrimitives,
geo-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
pi2: snd(t),
pi1: fst(t),
geo-line: Line,
geo-plsep: p # l,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
geo-primitives_wf,
geo-point_wf,
geo-line_wf,
geo-lsep_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
dependent_functionElimination,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
productElimination,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:GeometryPrimitives]. \mforall{}[p:Point]. \mforall{}[l:Line]. (p \# l \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-01_07_08
Last ObjectModification:
2018_05_21-AM-01_33_18
Theory : euclidean!plane!geometry
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