Nuprl Lemma : LP-sep-or2
∀g:ProjectivePlaneStructure. ∀l:Line. ∀p,q:Point. (p ≠ l ⇒ (q ≠ l ∨ q ≠ p))
Proof
Definitions occuring in Statement :
projective-plane-structure: ProjectivePlaneStructure,
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 :
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x],
pgeo-lpsep: a ≠ b,
guard: {T}
Lemmas referenced :
projective-plane-structure_wf,
pgeo-line_wf,
pgeo-point_wf,
projective-plane-structure_subtype,
pgeo-plsep_wf,
LP-sep-or
Rules used in proof :
because_Cache,
sqequalRule,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_functionElimination,
dependent_functionElimination
Latex:
\mforall{}g:ProjectivePlaneStructure. \mforall{}l:Line. \mforall{}p,q:Point. (p \mneq{} l {}\mRightarrow{} (q \mneq{} l \mvee{} q \mneq{} p))
Date html generated:
2018_05_22-PM-00_30_00
Last ObjectModification:
2017_11_15-PM-01_32_42
Theory : euclidean!plane!geometry
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