Nuprl Lemma : geo-Aparallel_wf
∀[e:EuclideanPlane]. ∀[l,m:LINE]. (l || m ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-Aparallel: l || m,
geoline: LINE,
euclidean-plane: EuclideanPlane,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
geo-Aparallel: l || m
Lemmas referenced :
not_wf,
geo-intersect_wf,
geoline_wf,
euclidean-plane_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{}[e:EuclideanPlane]. \mforall{}[l,m:LINE]. (l || m \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-01_07_41
Last ObjectModification:
2018_05_10-PM-06_03_37
Theory : euclidean!plane!geometry
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