Nuprl Lemma : eu-between-eq-implies-colinear

e:EuclideanStructure. ∀[a,b,c:Point].  (Colinear(a;b;c)) supposing (a_b_c and (a b ∈ Point)))


Definitions occuring in Statement :  eu-between-eq: a_b_c eu-colinear: Colinear(a;b;c) eu-point: Point euclidean-structure: EuclideanStructure uimplies: supposing a uall: [x:A]. B[x] all: x:A. B[x] not: ¬A equal: t ∈ T
Definitions unfolded in proof :  all: x:A. B[x] uall: [x:A]. B[x] uimplies: supposing a member: t ∈ T not: ¬A implies:  Q false: False stable: Stable{P} iff: ⇐⇒ Q and: P ∧ Q rev_implies:  Q prop: cand: c∧ B
Lemmas referenced :  eu-point_wf stable__colinear eu-between-eq-def eu-colinear-def and_wf not_wf equal_wf eu-between_wf eu-colinear_wf eu-between-eq_wf euclidean-structure_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation isect_memberFormation cut introduction sqequalRule sqequalHypSubstitution lambdaEquality dependent_functionElimination thin hypothesisEquality voidElimination equalityEquality lemma_by_obid isectElimination hypothesis rename independent_isectElimination productElimination independent_functionElimination addLevel impliesFunctionality levelHypothesis promote_hyp impliesLevelFunctionality independent_pairFormation

\mforall{}e:EuclideanStructure.  \mforall{}[a,b,c:Point].    (Colinear(a;b;c))  supposing  (a\_b\_c  and  (\mneg{}(a  =  b)))

Date html generated: 2016_05_18-AM-06_33_06
Last ObjectModification: 2015_12_28-AM-09_28_08

Theory : euclidean!geometry

Home Index