Nuprl Lemma : pgeo-plsep-to-lsep
∀g:ProjectivePlaneStructure. ∀a,b:Line. ∀l:Point. (l ≠ a ⇒ l I b ⇒ b ≠ a)
Proof
Definitions occuring in Statement :
projective-plane-structure: ProjectivePlaneStructure,
pgeo-lsep: l ≠ m,
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 :
pgeo-lsep: l ≠ m,
btrue: tt,
mk-pgeo-prim: mk-pgeo-prim,
bfalse: ff,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
top: Top,
mk-pgeo: mk-pgeo(p; ss; por; lor; j; m; p3; l3),
pgeo-dual-prim: pg*,
pgeo-point: Point,
pgeo-line: Line,
pgeo-plsep: a ≠ b,
pgeo-incident: a I b,
pgeo-psep: a ≠ b,
pgeo-dual: pg*,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
projective-plane-structure_wf,
rec_select_update_lemma,
pgeo-dual_wf,
pgeo-plsep-to-psep
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{}g:ProjectivePlaneStructure. \mforall{}a,b:Line. \mforall{}l:Point. (l \mneq{} a {}\mRightarrow{} l I b {}\mRightarrow{} b \mneq{} a)
Date html generated:
2018_05_22-PM-00_35_02
Last ObjectModification:
2017_11_25-AM-08_57_52
Theory : euclidean!plane!geometry
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