Nuprl Lemma : geo-midpoint_wf
∀[e:GeometryPrimitives]. ∀[m,a,b:Point]. (a=m=b ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-midpoint: a=m=b,
geo-primitives: GeometryPrimitives,
geo-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
and: P ∧ Q,
prop: ℙ,
geo-midpoint: a=m=b,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
geo-primitives_wf,
geo-point_wf,
geo-congruent_wf,
geo-between_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
productEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:GeometryPrimitives]. \mforall{}[m,a,b:Point]. (a=m=b \mmember{} \mBbbP{})
Date html generated:
2018_05_22-AM-11_52_10
Last ObjectModification:
2018_05_21-AM-01_12_55
Theory : euclidean!plane!geometry
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