Nuprl Lemma : pgeo-join-to-line_dual
∀g:BasicProjectivePlane. ∀p,q:Line. ∀l:Point. ∀s:p ≠ q. (l I p ⇒ l I q ⇒ p ∧ q ≡ l)
Proof
Definitions occuring in Statement :
basic-projective-plane: BasicProjectivePlane,
pgeo-meet: l ∧ m,
pgeo-peq: a ≡ b,
pgeo-lsep: l ≠ m,
pgeo-incident: a I b,
pgeo-line: Line,
pgeo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
pgeo-peq: a ≡ b,
pgeo-meet: l ∧ m,
mk-pgeo-prim: mk-pgeo-prim,
btrue: tt,
bfalse: ff,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
top: Top,
pgeo-plsep: a ≠ b,
pgeo-lsep: l ≠ m,
mk-pgeo: mk-pgeo(p; ss; por; lor; j; m; p3; l3),
pgeo-dual-prim: pg*,
pgeo-point: Point,
pgeo-line: Line,
pgeo-psep: a ≠ b,
pgeo-incident: a I b,
pgeo-leq: a ≡ b,
pgeo-join: p ∨ q,
pgeo-dual: pg*,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
basic-projective-plane_wf,
rec_select_update_lemma,
pgeo-dual_wf2,
pgeo-join-to-line
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:BasicProjectivePlane. \mforall{}p,q:Line. \mforall{}l:Point. \mforall{}s:p \mneq{} q. (l I p {}\mRightarrow{} l I q {}\mRightarrow{} p \mwedge{} q \mequiv{} l)
Date html generated:
2018_05_22-PM-00_35_48
Last ObjectModification:
2017_11_25-AM-09_11_39
Theory : euclidean!plane!geometry
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