Nuprl Lemma : pgeo-three-points_wf
∀g:ProjectivePlaneStructure. ∀l:Line.
(pgeo-three-point-axiom(l) ∈ ∃a,b,c:Point. (a I l ∧ b I l ∧ c I l ∧ a ≠ b ∧ b ≠ c ∧ c ≠ a))
Proof
Definitions occuring in Statement :
pgeo-three-points: pgeo-three-point-axiom(l),
projective-plane-structure: ProjectivePlaneStructure,
pgeo-psep: a ≠ b,
pgeo-incident: a I b,
pgeo-line: Line,
pgeo-point: Point,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q,
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
pgeo-three-points: pgeo-three-point-axiom(l),
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],
prop: ℙ,
or: P ∨ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
and: P ∧ Q
Latex:
\mforall{}g:ProjectivePlaneStructure. \mforall{}l:Line.
(pgeo-three-point-axiom(l) \mmember{} \mexists{}a,b,c:Point. (a I l \mwedge{} b I l \mwedge{} c I l \mwedge{} a \mneq{} b \mwedge{} b \mneq{} c \mwedge{} c \mneq{} a))
Date html generated:
2020_05_20-AM-10_37_10
Last ObjectModification:
2019_12_03-AM-09_49_07
Theory : euclidean!plane!geometry
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