Nuprl Lemma : geo-Aparallel-equiv2
∀e:EuclideanParPlane. EquivRel(LINE;l,m.l || m)
Proof
Definitions occuring in Statement :
euclidean-parallel-plane: EuclideanParPlane,
geo-Aparallel: l || m,
geoline: LINE,
equiv_rel: EquivRel(T;x,y.E[x; y]),
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
member: t ∈ T,
euclidean-parallel-plane: EuclideanParPlane,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
cand: A c∧ B,
sym: Sym(T;x,y.E[x; y]),
guard: {T},
prop: ℙ,
trans: Trans(T;x,y.E[x; y])
Lemmas referenced :
geo-Aparallel_weakening,
geoline_wf,
geo-Aparallel_inversion,
geo-Aparallel_wf,
geo-Aparallel_transitivity,
euclidean-parallel-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
independent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
because_Cache,
independent_functionElimination,
isectElimination
Latex:
\mforall{}e:EuclideanParPlane. EquivRel(LINE;l,m.l || m)
Date html generated:
2018_05_22-PM-01_11_15
Last ObjectModification:
2018_05_14-AM-11_50_56
Theory : euclidean!plane!geometry
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