Nuprl Lemma : pgeo-lsep-implies-plsep_dual
∀g:ProjectivePlane. ∀p:Line. ∀l,m:Point. ∀s:l ≠ m. (l I p ⇒ p ≠ l ∨ m ⇒ m ≠ p)
Proof
Definitions occuring in Statement :
projective-plane: ProjectivePlane,
pgeo-join: p ∨ q,
pgeo-lsep: l ≠ m,
pgeo-psep: a ≠ b,
pgeo-incident: a I b,
pgeo-plsep: a ≠ b,
pgeo-line: Line,
pgeo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
dual-plane: dual-plane(pg),
pgeo-plsep: a ≠ b,
pgeo-meet: l ∧ m,
pgeo-psep: a ≠ b,
pgeo-incident: a I b,
pgeo-lsep: l ≠ m,
pgeo-line: Line,
pgeo-point: Point,
complete-pgeo-dual: complete-pgeo-dual(pg;l),
pgeo-dual: pg*,
mk-complete-pgeo: mk-complete-pgeo(pg;p),
top: Top,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
pgeo-dual-prim: pg*,
mk-pgeo: mk-pgeo(p; ss; por; lor; j; m; p3; l3),
btrue: tt,
mk-pgeo-prim: mk-pgeo-prim,
pgeo-join: p ∨ q
Lemmas referenced :
pgeo-lsep-implies-plsep,
dual-plane_wf,
rec_select_update_lemma,
projective-plane_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
hypothesisEquality,
hypothesis,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}g:ProjectivePlane. \mforall{}p:Line. \mforall{}l,m:Point. \mforall{}s:l \mneq{} m. (l I p {}\mRightarrow{} p \mneq{} l \mvee{} m {}\mRightarrow{} m \mneq{} p)
Date html generated:
2018_05_22-PM-00_48_22
Last ObjectModification:
2017_12_05-AM-08_36_10
Theory : euclidean!plane!geometry
Home
Index