Nuprl Lemma : pgeo-meet_wf
∀g:ProjectivePlaneStructure. ∀l,m:Line. ∀s:l ≠ m. (l ∧ m ∈ {p:Point| p I l ∧ p I m} )
Proof
Definitions occuring in Statement :
pgeo-meet: l ∧ m,
projective-plane-structure: ProjectivePlaneStructure,
pgeo-lsep: l ≠ m,
pgeo-incident: a I b,
pgeo-line: Line,
pgeo-point: Point,
all: ∀x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]}
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
pgeo-meet: l ∧ m,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
projective-plane-structure: ProjectivePlaneStructure,
record+: record+,
record-select: r.x,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
or: P ∨ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
uimplies: b supposing a,
top: Top
Latex:
\mforall{}g:ProjectivePlaneStructure. \mforall{}l,m:Line. \mforall{}s:l \mneq{} m. (l \mwedge{} m \mmember{} \{p:Point| p I l \mwedge{} p I m\} )
Date html generated:
2020_05_20-AM-10_36_56
Last ObjectModification:
2019_12_03-AM-09_49_50
Theory : euclidean!plane!geometry
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