Nuprl Lemma : eu-nontrivial_wf

[e:EuclideanStructure]
  (eu-nontrivial(e) ∈ {triple:Point × Point × Point| let a,b,c triple in (a b ∈ Point)) ∧ Colinear(a;b;c))} )


Proof




Definitions occuring in Statement :  eu-nontrivial: eu-nontrivial(e) eu-colinear: Colinear(a;b;c) eu-point: Point euclidean-structure: EuclideanStructure spreadn: spread3 uall: [x:A]. B[x] not: ¬A and: P ∧ Q member: t ∈ T set: {x:A| B[x]}  product: x:A × B[x] equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T eu-nontrivial: eu-nontrivial(e) eu-colinear: Colinear(a;b;c) eu-point: Point euclidean-structure: EuclideanStructure record+: record+ record-select: r.x subtype_rel: A ⊆B eq_atom: =a y ifthenelse: if then else fi  btrue: tt guard: {T} prop: spreadn: spread3 and: P ∧ Q so_lambda: λ2x.t[x] so_apply: x[s] iff: ⇐⇒ Q rev_implies:  Q implies:  Q uimplies: supposing a all: x:A. B[x]
Lemmas referenced :  subtype_rel_self not_wf equal_wf uall_wf iff_wf and_wf isect_wf euclidean-structure_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule sqequalHypSubstitution dependentIntersectionElimination dependentIntersectionEqElimination thin hypothesis applyEquality tokenEquality instantiate lemma_by_obid isectElimination universeEquality functionEquality equalityTransitivity equalitySymmetry lambdaEquality cumulativity hypothesisEquality because_Cache setEquality productEquality productElimination setElimination rename lambdaFormation axiomEquality

Latex:
\mforall{}[e:EuclideanStructure]
    (eu-nontrivial(e)  \mmember{}  \{triple:Point  \mtimes{}  Point  \mtimes{}  Point| 
                                              let  a,b,c  =  triple  in 
                                              (\mneg{}(a  =  b))  \mwedge{}  (\mneg{}Colinear(a;b;c))\}  )



Date html generated: 2016_05_18-AM-06_32_31
Last ObjectModification: 2015_12_28-AM-09_28_40

Theory : euclidean!geometry


Home Index