Nuprl Lemma : geoline_wf
∀[e:EuclideanPlane]. (LINE ∈ Type)
Proof
Definitions occuring in Statement :
geoline: LINE,
euclidean-plane: EuclideanPlane,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
geoline: LINE,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
quotient_wf,
geo-line_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-line-eq_wf,
geo-line-eq-equiv
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
lambdaEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[e:EuclideanPlane]. (LINE \mmember{} Type)
Date html generated:
2018_05_22-PM-01_02_56
Last ObjectModification:
2018_05_10-PM-04_32_34
Theory : euclidean!plane!geometry
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