Nuprl Lemma : pgeo-unique_wf

∀g:ProjectivePlaneStructure. ∀l,m:Line. ∀p,q:Point.  (unique(lm,pq) ∈ ℙ)


Proof




Definitions occuring in Statement :  pgeo-unique: unique(lm,pq),  projective-plane-structure: ProjectivePlaneStructure,  pgeo-line: Line,  pgeo-point: Point,  prop: ℙ,  all: ∀x:A. B[x],  member: t ∈ T
Definitions unfolded in proof :  all: ∀x:A. B[x],  member: t ∈ T,  pgeo-unique: unique(lm,pq),  implies: P ⇒ Q,  prop: ℙ,  uall: ∀[x:A]. B[x],  subtype_rel: A ⊆r B,  and: P ∧ Q
Lemmas referenced :  pgeo-incident_wf,  projective-plane-structure_subtype,  not_wf,  pgeo-peq_wf,  pgeo-leq_wf,  pgeo-point_wf,  pgeo-line_wf,  projective-plane-structure_wf
Rules used in proof :  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  lambdaFormation,  cut,  sqequalRule,  functionEquality,  introduction,  extract_by_obid,  sqequalHypSubstitution,  isectElimination,  thin,  hypothesisEquality,  applyEquality,  hypothesis,  because_Cache,  productEquality

Latex:
\mforall{}g:ProjectivePlaneStructure.  \mforall{}l,m:Line.  \mforall{}p,q:Point.    (unique(lm,pq)  \mmember{}  \mBbbP{})



Date html generated: 2018_05_22-PM-00_32_38
Last ObjectModification: 2017_10_30-PM-01_52_29

Theory : euclidean!plane!geometry


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