Nuprl Lemma : geo-between-implies-colinear2
∀e:BasicGeometry. ∀[a,b,c:Point]. Colinear(a;b;c) supposing c_a_b
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-colinear: Colinear(a;b;c),
geo-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 :
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
false: False,
and: P ∧ Q,
implies: P ⇒ Q,
not: ¬A,
geo-colinear: Colinear(a;b;c),
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-between_wf,
not_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
independent_isectElimination,
instantiate,
dependent_functionElimination,
lambdaEquality,
sqequalRule,
because_Cache,
applyEquality,
hypothesisEquality,
isectElimination,
extract_by_obid,
productEquality,
voidElimination,
hypothesis,
independent_functionElimination,
thin,
productElimination,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}[a,b,c:Point]. Colinear(a;b;c) supposing c\_a\_b
Date html generated:
2017_10_02-PM-04_43_17
Last ObjectModification:
2017_08_05-AM-08_42_48
Theory : euclidean!plane!geometry
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