Nuprl Lemma : pgeo-three-points-axiom
∀g:ProjectivePlaneStructure. ∀l:Line. ∃a,b,c:Point. (a I l ∧ b I l ∧ c I l ∧ a ≠ b ∧ b ≠ c ∧ c ≠ a)
Proof
Definitions occuring in Statement :
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
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-line_wf,
pgeo-three-points_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{}l:Line. \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:
2018_05_22-PM-00_31_50
Last ObjectModification:
2017_11_27-PM-04_19_05
Theory : euclidean!plane!geometry
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