Nuprl Lemma : proj-point-sep_wf
∀[e:EuclideanParPlane]. ∀[p,q:Point + Line]. (proj-point-sep(e;p;q) ∈ ℙ)
Proof
Definitions occuring in Statement :
proj-point-sep: proj-point-sep(eu;p;q),
euclidean-parallel-plane: EuclideanParPlane,
geo-line: Line,
geo-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
union: left + right
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
proj-point-sep: proj-point-sep(eu;p;q),
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
euclidean-parallel-plane: EuclideanParPlane,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
geo-sep_wf,
true_wf,
equal_wf,
geo-intersect_wf,
geoline-subtype1,
geo-point_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
euclidean-planes-subtype,
subtype_rel_transitivity,
euclidean-parallel-plane_wf,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-line_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
thin,
because_Cache,
lambdaFormation,
unionElimination,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
applyEquality,
dependent_functionElimination,
independent_functionElimination,
setElimination,
rename,
axiomEquality,
unionEquality,
instantiate,
independent_isectElimination,
isect_memberEquality
Latex:
\mforall{}[e:EuclideanParPlane]. \mforall{}[p,q:Point + Line]. (proj-point-sep(e;p;q) \mmember{} \mBbbP{})
Date html generated:
2019_10_16-PM-02_42_53
Last ObjectModification:
2018_08_21-PM-02_00_32
Theory : euclidean!plane!geometry
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