Nuprl Lemma : pgeo-PLSepOr_wf
∀g:ProjectivePlaneStructure. ∀a:Point. ∀l:{l:Line| a ≠ l} . ∀m:Line. (PLSepOr(a;l;m) ∈ a ≠ m ∨ m ≠ l)
Proof
Definitions occuring in Statement :
pgeo-PLSepOr: PLSepOr(a;l;m),
projective-plane-structure: ProjectivePlaneStructure,
pgeo-lsep: l ≠ m,
pgeo-plsep: a ≠ b,
pgeo-line: Line,
pgeo-point: Point,
all: ∀x:A. B[x],
or: P ∨ Q,
member: t ∈ T,
set: {x:A| B[x]}
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
pgeo-PLSepOr: PLSepOr(a;l;m),
projective-plane-structure: ProjectivePlaneStructure,
record+: record+,
record-select: r.x,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
or: P ∨ Q,
sq_exists: ∃x:A [B[x]],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q
Lemmas referenced :
subtype_rel_self,
all_wf,
pgeo-line_wf,
pgeo-point_wf,
sq_stable_wf,
pgeo-plsep_wf,
or_wf,
pgeo-lsep_wf,
pgeo-psep_wf,
exists_wf,
sq_exists_wf,
pgeo-incident_wf,
projective-plane-structure_subtype,
set_wf,
projective-plane-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
setElimination,
thin,
rename,
sqequalRule,
sqequalHypSubstitution,
dependentIntersectionElimination,
dependentIntersectionEqElimination,
hypothesis,
applyEquality,
tokenEquality,
introduction,
extract_by_obid,
isectElimination,
lambdaEquality,
hypothesisEquality,
setEquality,
functionEquality,
productEquality,
because_Cache,
functionExtensionality,
dependent_set_memberEquality
Latex:
\mforall{}g:ProjectivePlaneStructure. \mforall{}a:Point. \mforall{}l:\{l:Line| a \mneq{} l\} . \mforall{}m:Line.
(PLSepOr(a;l;m) \mmember{} a \mneq{} m \mvee{} m \mneq{} l)
Date html generated:
2018_05_22-PM-00_29_12
Last ObjectModification:
2017_10_27-AM-08_47_02
Theory : euclidean!plane!geometry
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