Nuprl Lemma : pgeo-lsep-implies-plsep-or
∀g:ProjectivePlane. ∀p:Point. ∀l,m:Line. ∀s:l ≠ m. (p ≠ l ∧ m ⇒ (p ≠ m ∨ p ≠ l))
Proof
Definitions occuring in Statement :
projective-plane: ProjectivePlane,
pgeo-meet: l ∧ m,
pgeo-lsep: l ≠ m,
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 :
uimplies: b supposing a,
pgeo-psep: a ≠ b,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
or: P ∨ Q,
and: P ∧ Q,
exists: ∃x:A. B[x],
pgeo-lsep: l ≠ m,
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
pgeo-line_wf,
pgeo-lsep_wf,
pgeo-incident_wf,
pgeo-point_wf,
pgeo-meet_wf,
pgeo-primitives_wf,
projective-plane-structure_wf,
projective-plane-structure-complete_wf,
projective-plane_wf,
subtype_rel_transitivity,
projective-plane-subtype,
projective-plane-structure-complete_subtype,
projective-plane-structure_subtype,
pgeo-psep_wf,
pgeo-plsep_wf,
LP-sep-or2,
pgeo-meet-incident,
pgeo-plsep-to-lsep,
pgeo-meet-plsep-sym,
pgeo-plsep-to-psep,
pgeo-psep-or,
pgeo-lsep-implies-plsep,
Error :pgeo-psep-sym,
pgeo-meet-psep-sym
Rules used in proof :
productEquality,
setEquality,
setElimination,
lambdaEquality,
independent_isectElimination,
instantiate,
applyEquality,
isectElimination,
inrFormation,
sqequalRule,
unionElimination,
because_Cache,
rename,
productElimination,
hypothesis,
independent_functionElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
inlFormation
Latex:
\mforall{}g:ProjectivePlane. \mforall{}p:Point. \mforall{}l,m:Line. \mforall{}s:l \mneq{} m. (p \mneq{} l \mwedge{} m {}\mRightarrow{} (p \mneq{} m \mvee{} p \mneq{} l))
Date html generated:
2018_05_22-PM-00_52_51
Last ObjectModification:
2017_11_28-PM-05_27_58
Theory : euclidean!plane!geometry
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