Nuprl Lemma : pgeo-join-plsep-sym
∀pg:ProjectivePlane. ∀a,b,c:Point. ∀s:a ≠ b. ∀s2:b ≠ a. (c ≠ a ∨ b ⇒ c ≠ b ∨ a)
Proof
Definitions occuring in Statement :
projective-plane: ProjectivePlane,
pgeo-join: p ∨ q,
pgeo-psep: a ≠ b,
pgeo-plsep: a ≠ b,
pgeo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
guard: {T},
uimplies: b supposing a,
and: P ∧ Q,
prop: ℙ,
or: P ∨ Q,
pgeo-lsep: l ≠ m,
exists: ∃x:A. B[x],
pgeo-incident: a I b,
not: ¬A,
false: False
Lemmas referenced :
PL-sep-or,
pgeo-join_wf,
projective-plane-structure-complete_subtype,
projective-plane-subtype,
subtype_rel_transitivity,
projective-plane_wf,
projective-plane-structure-complete_wf,
projective-plane-structure_wf,
pgeo-line_wf,
pgeo-incident_wf,
pgeo-join-lsep-sym,
pgeo-plsep_wf,
projective-plane-structure_subtype,
pgeo-primitives_wf,
pgeo-psep_wf,
pgeo-point_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
because_Cache,
hypothesisEquality,
applyEquality,
hypothesis,
instantiate,
isectElimination,
independent_isectElimination,
sqequalRule,
lambdaEquality,
setElimination,
rename,
setEquality,
productEquality,
independent_functionElimination,
unionElimination,
productElimination,
voidElimination
Latex:
\mforall{}pg:ProjectivePlane. \mforall{}a,b,c:Point. \mforall{}s:a \mneq{} b. \mforall{}s2:b \mneq{} a. (c \mneq{} a \mvee{} b {}\mRightarrow{} c \mneq{} b \mvee{} a)
Date html generated:
2018_05_22-PM-00_49_01
Last ObjectModification:
2017_12_05-AM-11_23_23
Theory : euclidean!plane!geometry
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