Nuprl Lemma : geo-colinear_wf
∀[e:GeometryPrimitives]. ∀[a,b,c:Point]. (Colinear(a;b;c) ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-colinear: Colinear(a;b;c),
geo-primitives: GeometryPrimitives,
geo-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
geo-colinear: Colinear(a;b;c),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
geo-primitives_wf,
geo-point_wf,
geo-lsep_wf,
not_wf
Rules used in proof :
universeIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
inhabitedIsType,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:GeometryPrimitives]. \mforall{}[a,b,c:Point]. (Colinear(a;b;c) \mmember{} \mBbbP{})
Date html generated:
2019_10_29-AM-09_12_44
Last ObjectModification:
2019_10_25-PM-01_32_00
Theory : euclidean!plane!geometry
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