Nuprl Lemma : pgeo-three-lines-axiom
∀g:ProjectivePlaneStructure. ∀p:Point. ∃l,m,n:Line. (p I l ∧ p I m ∧ p I n ∧ l ≠ m ∧ m ≠ n ∧ n ≠ l)
Proof
Definitions occuring in Statement :
projective-plane-structure: ProjectivePlaneStructure,
pgeo-lsep: l ≠ m,
pgeo-incident: a I b,
pgeo-line: Line,
pgeo-point: Point,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
and: P ∧ Q
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
projective-plane-structure_wf,
projective-plane-structure_subtype,
pgeo-point_wf,
pgeo-three-lines_wf
Rules used in proof :
sqequalRule,
applyEquality,
isectElimination,
hypothesis,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:ProjectivePlaneStructure. \mforall{}p:Point. \mexists{}l,m,n:Line. (p I l \mwedge{} p I m \mwedge{} p I n \mwedge{} l \mneq{} m \mwedge{} m \mneq{} n \mwedge{} n \mneq{} l)
Date html generated:
2018_05_22-PM-00_32_18
Last ObjectModification:
2017_11_27-PM-04_18_48
Theory : euclidean!plane!geometry
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