Nuprl Lemma : lsep-all-sym2
∀g:EuclideanPlane. ∀a,b,c:Point. (a leftof bc ⇒ {a # bc ∧ b # ca ∧ c # ab ∧ a # cb ∧ b # ac ∧ c # ba})
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-lsep: a # bc,
geo-left: a leftof bc,
geo-point: Point,
guard: {T},
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
geo-lsep: a # bc,
or: P ∨ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
and: P ∧ Q,
cand: A c∧ B,
uimplies: b supposing a
Lemmas referenced :
lsep-all-sym,
geo-left_wf,
geo-point_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
inlFormation,
isectElimination,
applyEquality,
because_Cache,
sqequalRule,
independent_functionElimination,
productElimination,
independent_pairFormation,
instantiate,
independent_isectElimination
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b,c:Point.
(a leftof bc {}\mRightarrow{} \{a \# bc \mwedge{} b \# ca \mwedge{} c \# ab \mwedge{} a \# cb \mwedge{} b \# ac \mwedge{} c \# ba\})
Date html generated:
2018_05_22-AM-11_53_53
Last ObjectModification:
2018_03_26-PM-02_37_26
Theory : euclidean!plane!geometry
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