Nuprl Lemma : geo-be-compress

e:BasicGeometry. ∀a,b,c:Point.  (a_b_c  a_c_b  b ≡ c)


Proof




Definitions occuring in Statement :  basic-geometry: BasicGeometry geo-eq: a ≡ b geo-between: a_b_c geo-point: Point all: x:A. B[x] implies:  Q
Definitions unfolded in proof :  uimplies: supposing a guard: {T} subtype_rel: A ⊆B uall: [x:A]. B[x] prop: member: t ∈ T implies:  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-between_wf geo-between-exchange3 geo-between-same
Rules used in proof :  because_Cache sqequalRule independent_isectElimination instantiate hypothesis applyEquality hypothesisEquality thin isectElimination sqequalHypSubstitution extract_by_obid introduction cut lambdaFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution dependent_functionElimination

Latex:
\mforall{}e:BasicGeometry.  \mforall{}a,b,c:Point.    (a\_b\_c  {}\mRightarrow{}  a\_c\_b  {}\mRightarrow{}  b  \mequiv{}  c)



Date html generated: 2017_10_02-PM-06_37_50
Last ObjectModification: 2017_08_05-PM-04_46_29

Theory : euclidean!plane!geometry


Home Index