Nuprl Lemma : dual-line-subtype
∀[pg:BasicProjectivePlane]. (Line ⊆r Point)
Proof
Definitions occuring in Statement :
basic-projective-plane: BasicProjectivePlane,
pgeo-dual: pg*,
pgeo-line: Line,
pgeo-point: Point,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
pgeo-point: Point,
btrue: tt,
mk-pgeo-prim: mk-pgeo-prim,
pgeo-dual-prim: pg*,
bfalse: ff,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
record-update: r[x := v],
mk-pgeo: mk-pgeo(p; ss; por; lor; j; m; p3; l3),
pgeo-dual: pg*,
record-select: r.x,
pgeo-line: Line,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
pgeo-primitives_wf,
projective-plane-structure_wf,
basic-projective-plane_wf,
subtype_rel_transitivity,
basic-projective-plane-subtype,
projective-plane-structure_subtype,
pgeo-point_wf,
subtype_rel_self
Rules used in proof :
axiomEquality,
independent_isectElimination,
instantiate,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
hypothesis,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[pg:BasicProjectivePlane]. (Line \msubseteq{}r Point)
Date html generated:
2018_05_22-PM-00_34_34
Last ObjectModification:
2017_12_01-PM-05_17_24
Theory : euclidean!plane!geometry
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