Nuprl Lemma : eu-bisect-line_wf
∀[e:EuclideanPlane]. ∀[a,b:Point]. (eu-bisect-line(e;a;b) ∈ ℙ)
Proof
Definitions occuring in Statement :
eu-bisect-line: eu-bisect-line(e;a;b),
euclidean-plane: EuclideanPlane,
eu-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
exists: ∃x:A. B[x],
so_apply: x[s],
so_lambda: λ2x.t[x],
euclidean-plane: EuclideanPlane,
and: P ∧ Q,
prop: ℙ,
eu-bisect-line: eu-bisect-line(e;a;b),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
lambdaEquality,
hypothesisEquality,
hypothesis,
because_Cache,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
productEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[a,b:Point]. (eu-bisect-line(e;a;b) \mmember{} \mBbbP{})
Date html generated:
2016_07_08-PM-05_54_25
Last ObjectModification:
2016_07_05-PM-03_04_18
Theory : euclidean!geometry
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