Nuprl Lemma : geo-interior-point_wf
∀[e:EuclideanPlane]. ∀[a,b,c,d:Point]. (I(abc;d) ∈ ℙ)
Proof
Definitions occuring in Statement :
geo-interior-point: I(abc;d),
euclidean-plane: EuclideanPlane,
geo-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
geo-interior-point: I(abc;d),
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
geo-left_wf,
geo-point_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType,
instantiate,
independent_isectElimination
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[a,b,c,d:Point]. (I(abc;d) \mmember{} \mBbbP{})
Date html generated:
2019_10_16-PM-02_20_19
Last ObjectModification:
2019_03_19-PM-04_50_07
Theory : euclidean!plane!geometry
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