Nuprl Lemma : geo-strict-between-trans3
∀e:BasicGeometry. ∀a,b,c,d:Point. (a-b-c ⇒ b-c-d ⇒ a-c-d)
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 :
prop: ℙ,
cand: A c∧ B,
guard: {T},
subtype_rel: A ⊆r B,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
geo-strict-between: a-b-c,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
geo-point_wf,
geo-strict-between_wf,
geo-strict-between-sep1,
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-strict-between-sep3,
geo-between-outer-trans,
geo-strict-between-implies-between
Rules used in proof :
independent_functionElimination,
sqequalRule,
instantiate,
applyEquality,
hypothesisEquality,
hypothesis,
independent_isectElimination,
isectElimination,
because_Cache,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c,d:Point. (a-b-c {}\mRightarrow{} b-c-d {}\mRightarrow{} a-c-d)
Date html generated:
2017_10_02-PM-04_51_33
Last ObjectModification:
2017_08_05-AM-09_08_18
Theory : euclidean!plane!geometry
Home
Index