### Nuprl Lemma : eu-middle_wf

`∀[e:EuclideanStructure]. ∀[a,b:Point]. ∀[c:{c:Point| ¬Colinear(a;b;c)} ].  (middle(a;b;c) ∈ Point)`

Proof

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

Latex:
\mforall{}[e:EuclideanStructure].  \mforall{}[a,b:Point].  \mforall{}[c:\{c:Point|  \mneg{}Colinear(a;b;c)\}  ].    (middle(a;b;c)  \mmember{}  Point)

Date html generated: 2016_10_26-AM-07_40_46
Last ObjectModification: 2016_09_20-PM-08_00_47

Theory : euclidean!geometry

Home Index