Nuprl Lemma : geoline-subtype2
∀[e:EuclideanParPlane]. (LINE ⊆r (l,m:Line//l || m))
Proof
Definitions occuring in Statement :
euclidean-parallel-plane: EuclideanParPlane,
geo-Aparallel: l || m,
geoline: LINE,
geo-line: Line,
quotient: x,y:A//B[x; y],
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
geoline: LINE,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
guard: {T},
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
euclidean-parallel-plane_wf,
geo-line_wf,
euclidean-plane-structure-subtype,
subtype_rel_transitivity,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-line-eq_wf,
geo-Aparallel_wf,
geoline-subtype1,
subtype_rel_self,
geo-Aparallel-equiv,
geo-line-eq-equiv,
quotient_subtype_quotient,
quotient-member-eq,
euclidean-planes-subtype,
geo-Aparallel_weakening
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
axiomEquality,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
applyEquality,
instantiate,
isectElimination,
independent_isectElimination,
lambdaEquality,
because_Cache,
lambdaFormation,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[e:EuclideanParPlane]. (LINE \msubseteq{}r (l,m:Line//l || m))
Date html generated:
2018_05_22-PM-01_11_26
Last ObjectModification:
2018_05_11-PM-01_52_46
Theory : euclidean!plane!geometry
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