Nuprl Lemma : not-geo-strict-between-same2
∀e:BasicGeometry. ∀[a,b:Point]. False supposing a-a-b
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-strict-between: a-b-c,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
false: False
Definitions unfolded in proof :
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
implies: P ⇒ Q,
false: False,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
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,
not-geo-strict-between-same,
geo-strict-between-sym
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
instantiate,
applyEquality,
sqequalRule,
voidElimination,
independent_isectElimination,
isectElimination,
hypothesis,
independent_functionElimination,
because_Cache,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}[a,b:Point]. False supposing a-a-b
Date html generated:
2017_10_02-PM-04_42_42
Last ObjectModification:
2017_08_05-AM-08_41_47
Theory : euclidean!plane!geometry
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