Nuprl Lemma : P_line_wf
∀e:EuclideanParPlane. (P_line(e) ∈ Type)
Proof
Definitions occuring in Statement :
P_line: P_line(eu),
euclidean-parallel-plane: EuclideanParPlane,
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
P_line: P_line(eu),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
guard: {T},
uimplies: b supposing a,
euclidean-parallel-plane: EuclideanParPlane,
prop: ℙ
Lemmas referenced :
geo-line_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-point_wf,
geo-incident_wf,
geoline-subtype1,
geo-plsep_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
productEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
instantiate,
isectElimination,
independent_isectElimination,
because_Cache,
setEquality,
setElimination,
rename
Latex:
\mforall{}e:EuclideanParPlane. (P\_line(e) \mmember{} Type)
Date html generated:
2019_10_16-PM-03_00_14
Last ObjectModification:
2018_08_08-PM-06_05_11
Theory : euclidean!plane!geometry
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