Nuprl Lemma : PL-sep-or
∀g:ProjectivePlaneStructure. ∀a:Point. ∀l,m:Line. (a ≠ l ⇒ (a ≠ m ∨ m ≠ l))
Proof
Definitions occuring in Statement :
projective-plane-structure: ProjectivePlaneStructure,
pgeo-lsep: l ≠ m,
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 :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
pgeo-PLSepOr_wf,
pgeo-plsep_wf,
projective-plane-structure_subtype,
pgeo-line_wf,
pgeo-point_wf,
projective-plane-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality,
hypothesis,
isectElimination,
applyEquality,
because_Cache,
sqequalRule
Latex:
\mforall{}g:ProjectivePlaneStructure. \mforall{}a:Point. \mforall{}l,m:Line. (a \mneq{} l {}\mRightarrow{} (a \mneq{} m \mvee{} m \mneq{} l))
Date html generated:
2018_05_22-PM-00_29_39
Last ObjectModification:
2017_11_10-PM-04_56_57
Theory : euclidean!plane!geometry
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