Nuprl Lemma : geo-strict-between-trans
∀e:BasicGeometry-. ∀a,b,c,d:Point.  (a-b-d 
⇒ b-c-d 
⇒ a-b-c)
Proof
Definitions occuring in Statement : 
basic-geometry-: BasicGeometry-
, 
geo-strict-between: a-b-c
, 
geo-point: Point
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
Definitions unfolded in proof : 
uimplies: b supposing a
, 
guard: {T}
, 
subtype_rel: A ⊆r B
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
squash: ↓T
, 
basic-geo-axioms: BasicGeometryAxioms(g)
, 
cand: A c∧ B
, 
and: P ∧ Q
, 
geo-strict-between: a-b-c
, 
sq_stable: SqStable(P)
, 
member: t ∈ T
, 
basic-geometry-: BasicGeometry-
, 
implies: P 
⇒ Q
, 
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, 
sq_stable__geo-strict-between
Rules used in proof : 
because_Cache, 
independent_isectElimination, 
instantiate, 
applyEquality, 
isectElimination, 
imageElimination, 
baseClosed, 
imageMemberEquality, 
sqequalRule, 
independent_pairFormation, 
productElimination, 
independent_functionElimination, 
hypothesis, 
hypothesisEquality, 
dependent_functionElimination, 
extract_by_obid, 
introduction, 
cut, 
rename, 
thin, 
setElimination, 
sqequalHypSubstitution, 
lambdaFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry-.  \mforall{}a,b,c,d:Point.    (a-b-d  {}\mRightarrow{}  b-c-d  {}\mRightarrow{}  a-b-c)
Date html generated:
2017_10_02-PM-04_42_11
Last ObjectModification:
2017_08_05-AM-08_41_28
Theory : euclidean!plane!geometry
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