Nuprl Lemma : pgeo-join-lsep-sym
∀pg:ProjectivePlane. ∀l,m:Point. ∀a:Line. ∀s:l ≠ m. ∀s2:m ≠ l. (l ∨ m ≠ a ⇒ m ∨ l ≠ a)
Proof
Definitions occuring in Statement :
projective-plane: ProjectivePlane,
pgeo-join: p ∨ q,
pgeo-lsep: l ≠ m,
pgeo-psep: a ≠ b,
pgeo-line: Line,
pgeo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
pgeo-join: p ∨ q,
mk-pgeo-prim: mk-pgeo-prim,
btrue: tt,
mk-pgeo: mk-pgeo(p; ss; por; lor; j; m; p3; l3),
pgeo-dual-prim: pg*,
bfalse: ff,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
top: Top,
mk-complete-pgeo: mk-complete-pgeo(pg;p),
pgeo-dual: pg*,
pgeo-incident: a I b,
pgeo-plsep: a ≠ b,
complete-pgeo-dual: complete-pgeo-dual(pg;l),
pgeo-line: Line,
pgeo-point: Point,
pgeo-lsep: l ≠ m,
pgeo-psep: a ≠ b,
pgeo-meet: l ∧ m,
dual-plane: dual-plane(pg),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
projective-plane_wf,
rec_select_update_lemma,
dual-plane_wf,
pgeo-meet-psep-sym
Rules used in proof :
voidEquality,
voidElimination,
isect_memberEquality,
sqequalRule,
hypothesis,
hypothesisEquality,
isectElimination,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}pg:ProjectivePlane. \mforall{}l,m:Point. \mforall{}a:Line. \mforall{}s:l \mneq{} m. \mforall{}s2:m \mneq{} l. (l \mvee{} m \mneq{} a {}\mRightarrow{} m \mvee{} l \mneq{} a)
Date html generated:
2018_05_22-PM-00_48_52
Last ObjectModification:
2017_12_01-PM-05_57_17
Theory : euclidean!plane!geometry
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