Nuprl Lemma : pp-sep_wf
∀[eu:EuclideanParPlane]. ∀[p:Point + Line]. ∀[l:Line?]. (pp-sep(eu;p;l) ∈ ℙ)
Proof
Definitions occuring in Statement :
pp-sep: pp-sep(eu;p;l),
euclidean-parallel-plane: EuclideanParPlane,
geo-line: Line,
geo-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
unit: Unit,
member: t ∈ T,
union: left + right
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
all: ∀x:A. B[x],
euclidean-parallel-plane: EuclideanParPlane,
subtype_rel: A ⊆r B,
pp-sep: pp-sep(eu;p;l),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
geo-point_wf,
unit_wf2,
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
euclidean-parallel-plane_wf,
subtype_rel_transitivity,
euclidean-planes-subtype,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
geo-line_wf,
false_wf,
geoline-subtype1,
geo-intersect_wf,
true_wf,
geo-plsep_wf
Rules used in proof :
isect_memberEquality,
independent_isectElimination,
instantiate,
dependent_functionElimination,
unionEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
rename,
setElimination,
hypothesis,
because_Cache,
applyEquality,
hypothesisEquality,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
thin,
unionElimination,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[eu:EuclideanParPlane]. \mforall{}[p:Point + Line]. \mforall{}[l:Line?]. (pp-sep(eu;p;l) \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-01_13_07
Last ObjectModification:
2018_05_21-AM-09_51_16
Theory : euclidean!plane!geometry
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