Nuprl Lemma : geo-Aparallel_sym
∀e:EuclideanPlane. ∀l,m:LINE. (l || m ⇒ m || l)
Proof
Definitions occuring in Statement :
geo-Aparallel: l || m,
geoline: LINE,
euclidean-plane: EuclideanPlane,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
geo-Aparallel: l || m,
not: ¬A,
member: t ∈ T,
false: False,
prop: ℙ,
uall: ∀[x:A]. B[x]
Lemmas referenced :
geo-intersect-symmetry,
geo-intersect_wf,
geo-Aparallel_wf,
geoline_wf,
euclidean-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
introduction,
independent_functionElimination,
thin,
cut,
extract_by_obid,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
voidElimination,
isectElimination
Latex:
\mforall{}e:EuclideanPlane. \mforall{}l,m:LINE. (l || m {}\mRightarrow{} m || l)
Date html generated:
2018_05_22-PM-01_10_11
Last ObjectModification:
2018_05_10-PM-06_35_55
Theory : euclidean!plane!geometry
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