Nuprl Lemma : psep-join-implies-false
∀g:ProjectivePlaneStructure. ∀p,q:Point. ∀s:p ≠ q. (p ≠ p ∨ q ⇒ False)
Proof
Definitions occuring in Statement :
pgeo-join: p ∨ q,
projective-plane-structure: ProjectivePlaneStructure,
pgeo-psep: a ≠ b,
pgeo-plsep: a ≠ b,
pgeo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
false: False
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
false: False,
member: t ∈ T,
pgeo-incident: a I b,
not: ¬A,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
and: P ∧ Q
Lemmas referenced :
incident-join-first,
pgeo-plsep_wf,
projective-plane-structure_subtype,
pgeo-join_wf,
pgeo-line_wf,
pgeo-incident_wf,
pgeo-psep_wf,
pgeo-point_wf,
projective-plane-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
voidElimination,
isectElimination,
applyEquality,
sqequalRule,
lambdaEquality,
setElimination,
rename,
setEquality,
productEquality,
because_Cache
Latex:
\mforall{}g:ProjectivePlaneStructure. \mforall{}p,q:Point. \mforall{}s:p \mneq{} q. (p \mneq{} p \mvee{} q {}\mRightarrow{} False)
Date html generated:
2018_05_22-PM-00_35_20
Last ObjectModification:
2017_12_05-AM-09_01_21
Theory : euclidean!plane!geometry
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