Nuprl Lemma : left-all-symmetry
∀g:EuclideanPlane. ∀a,b,c:Point. (a leftof bc ⇒ {b leftof ca ∧ c leftof ab})
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
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 :
guard: {T},
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a
Lemmas referenced :
euclidean-plane-axioms,
geo-left_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-point_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
independent_functionElimination,
hypothesis,
independent_pairFormation,
isectElimination,
applyEquality,
instantiate,
independent_isectElimination,
because_Cache
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b,c:Point. (a leftof bc {}\mRightarrow{} \{b leftof ca \mwedge{} c leftof ab\})
Date html generated:
2018_05_22-AM-11_53_49
Last ObjectModification:
2018_04_17-PM-03_21_35
Theory : euclidean!plane!geometry
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