Nuprl Lemma : complete-pgeo-dual_wf
∀[pg:ProjectivePlaneStructure]. ∀[l:Line]. (complete-pgeo-dual(pg;l) ∈ ProjectivePlaneStructureComplete)
Proof
Definitions occuring in Statement :
complete-pgeo-dual: complete-pgeo-dual(pg;l),
projective-plane-structure-complete: ProjectivePlaneStructureComplete,
projective-plane-structure: ProjectivePlaneStructure,
pgeo-line: Line,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
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*,
pgeo-point: Point,
record-select: r.x,
pgeo-line: Line,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
complete-pgeo-dual: complete-pgeo-dual(pg;l),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
projective-plane-structure_wf,
pgeo-line_wf,
projective-plane-structure_subtype,
pgeo-point_wf,
subtype_rel-equal,
pgeo-dual_wf,
mk-complete-pgeo_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
independent_isectElimination,
because_Cache,
applyEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[pg:ProjectivePlaneStructure]. \mforall{}[l:Line].
(complete-pgeo-dual(pg;l) \mmember{} ProjectivePlaneStructureComplete)
Date html generated:
2018_05_22-PM-00_28_53
Last ObjectModification:
2017_11_27-PM-04_03_40
Theory : euclidean!plane!geometry
Home
Index