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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