Nuprl Lemma : geo-strict-between-same
∀[e:BasicGeometry-]. ∀[a,b:Point]. (¬a-b-a)
Proof
Definitions occuring in Statement :
basic-geometry-: BasicGeometry-,
geo-strict-between: a-b-c,
geo-point: Point,
uall: ∀[x:A]. B[x],
not: ¬A
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
false: False,
implies: P ⇒ Q,
not: ¬A,
member: t ∈ T,
uall: ∀[x:A]. B[x],
geo-eq: a ≡ b
Lemmas referenced :
geo-strict-between-sep1,
geo-point_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry-_wf,
subtype_rel_transitivity,
basic-geometry--subtype,
geo-strict-between_wf,
geo-eq_weakening
Rules used in proof :
isect_memberEquality,
dependent_functionElimination,
lambdaEquality,
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
hypothesisEquality,
isectElimination,
extract_by_obid,
voidElimination,
independent_functionElimination,
sqequalHypSubstitution,
hypothesis,
because_Cache,
thin,
lambdaFormation,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[e:BasicGeometry-]. \mforall{}[a,b:Point]. (\mneg{}a-b-a)
Date html generated:
2017_10_02-PM-04_42_34
Last ObjectModification:
2017_08_05-AM-08_41_43
Theory : euclidean!plane!geometry
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