Nuprl Lemma : geo-strict-between-implies-colinear
∀e:BasicGeometry. ∀[a,b,c:Point]. Colinear(a;b;c) supposing a-b-c
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-colinear: Colinear(a;b;c),
geo-strict-between: a-b-c,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
geo-strict-between: a-b-c,
prop: ℙ,
guard: {T},
subtype_rel: A ⊆r B,
and: P ∧ Q,
false: False,
implies: P ⇒ Q,
not: ¬A,
geo-colinear: Colinear(a;b;c),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
geo-point_wf,
geo-strict-between_wf,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-between_wf,
not_wf,
geo-between-implies-colinear
Rules used in proof :
productElimination,
because_Cache,
instantiate,
applyEquality,
productEquality,
voidElimination,
lambdaEquality,
sqequalRule,
independent_isectElimination,
isectElimination,
isect_memberFormation,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
hypothesis,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}e:BasicGeometry. \mforall{}[a,b,c:Point]. Colinear(a;b;c) supposing a-b-c
Date html generated:
2017_10_02-PM-04_43_14
Last ObjectModification:
2017_08_05-AM-08_42_46
Theory : euclidean!plane!geometry
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