Nuprl Lemma : pgeo-meet-psep-sym
∀g:ProjectivePlane. ∀l,m:Line. ∀a:Point. ∀s:l ≠ m. ∀s2:m ≠ l. (l ∧ m ≠ a ⇒ m ∧ l ≠ a)
Proof
Definitions occuring in Statement :
projective-plane: ProjectivePlane,
pgeo-meet: l ∧ m,
pgeo-lsep: l ≠ m,
pgeo-psep: a ≠ b,
pgeo-line: Line,
pgeo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uimplies: b supposing a,
false: False,
not: ¬A,
pgeo-incident: a I b,
or: P ∨ Q,
guard: {T},
prop: ℙ,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
projective-plane: ProjectivePlane,
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
pgeo-line_wf,
pgeo-lsep_wf,
pgeo-primitives_wf,
projective-plane-structure_wf,
basic-projective-plane_wf,
projective-plane_wf,
subtype_rel_transitivity,
projective-plane-subtype,
basic-projective-plane-subtype,
projective-plane-structure_subtype,
pgeo-psep_wf,
pgeo-meet-incident,
pgeo-lsep-implies-plsep,
pgeo-incident_wf,
pgeo-point_wf,
pgeo-meet_wf,
pgeo-psep-or
Rules used in proof :
independent_isectElimination,
instantiate,
voidElimination,
productElimination,
unionElimination,
independent_functionElimination,
productEquality,
sqequalRule,
isectElimination,
setEquality,
lambdaEquality,
applyEquality,
hypothesis,
because_Cache,
rename,
setElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:ProjectivePlane. \mforall{}l,m:Line. \mforall{}a:Point. \mforall{}s:l \mneq{} m. \mforall{}s2:m \mneq{} l. (l \mwedge{} m \mneq{} a {}\mRightarrow{} m \mwedge{} l \mneq{} a)
Date html generated:
2018_05_22-PM-00_46_47
Last ObjectModification:
2017_11_20-PM-03_10_51
Theory : euclidean!plane!geometry
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