Nuprl Lemma : pgeo-meet-plsep-sym
∀g:ProjectivePlane. ∀l,m,n:Line. ∀s:l ≠ m. ∀s2:m ≠ l. (l ∧ m ≠ n ⇒ m ∧ l ≠ n)
Proof
Definitions occuring in Statement :
projective-plane: ProjectivePlane,
pgeo-meet: l ∧ m,
pgeo-lsep: l ≠ m,
pgeo-plsep: a ≠ b,
pgeo-line: Line,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
or: P ∨ Q,
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],
false: False
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-plsep_wf,
pgeo-incident_wf,
pgeo-point_wf,
pgeo-meet_wf,
LP-sep-or2,
pgeo-meet-psep-implies-false
Rules used in proof :
independent_isectElimination,
instantiate,
unionElimination,
independent_functionElimination,
productEquality,
sqequalRule,
isectElimination,
setEquality,
lambdaEquality,
applyEquality,
hypothesis,
rename,
setElimination,
hypothesisEquality,
because_Cache,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
voidElimination
Latex:
\mforall{}g:ProjectivePlane. \mforall{}l,m,n:Line. \mforall{}s:l \mneq{} m. \mforall{}s2:m \mneq{} l. (l \mwedge{} m \mneq{} n {}\mRightarrow{} m \mwedge{} l \mneq{} n)
Date html generated:
2018_05_22-PM-00_47_07
Last ObjectModification:
2017_11_20-PM-03_17_54
Theory : euclidean!plane!geometry
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