Nuprl Lemma : LP-sep-or
∀g:ProjectivePlaneStructure. ∀l:Line. ∀p:Point. (l ≠ p ⇒ (∀q:Point. (q ≠ l ∨ q ≠ p)))
Proof
Definitions occuring in Statement :
projective-plane-structure: ProjectivePlaneStructure,
pgeo-lpsep: a ≠ b,
pgeo-psep: a ≠ b,
pgeo-plsep: a ≠ b,
pgeo-line: Line,
pgeo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q
Definitions unfolded in proof :
prop: ℙ,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
projective-plane-structure_wf,
pgeo-line_wf,
projective-plane-structure_subtype,
pgeo-point_wf,
pgeo-lpsep_wf,
pgeo-LPSepOr_wf
Rules used in proof :
sqequalRule,
because_Cache,
applyEquality,
isectElimination,
hypothesis,
dependent_set_memberEquality,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:ProjectivePlaneStructure. \mforall{}l:Line. \mforall{}p:Point. (l \mneq{} p {}\mRightarrow{} (\mforall{}q:Point. (q \mneq{} l \mvee{} q \mneq{} p)))
Date html generated:
2018_05_22-PM-00_29_49
Last ObjectModification:
2017_11_27-PM-04_19_25
Theory : euclidean!plane!geometry
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