### Nuprl Lemma : eu-inner-pasch_wf

`∀[e:EuclideanStructure]. ∀[a,b:Point]. ∀[c:{c:Point| ¬Colinear(a;b;c)} ]. ∀[p:{p:Point| a-p-c} ]. ∀[q:{q:Point| b_q_c} ]\000C.`
`  (eu-inner-pasch(e;a;b;c;p;q) ∈ Point)`

Proof

Definitions occuring in Statement :  eu-inner-pasch: `eu-inner-pasch(e;a;b;c;p;q)` eu-between-eq: `a_b_c` eu-colinear: `Colinear(a;b;c)` eu-between: `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-inner-pasch: `eu-inner-pasch(e;a;b;c;p;q)` eu-between-eq: `a_b_c` eu-point: `Point` eu-between: `a-b-c` eu-colinear: `Colinear(a;b;c)` 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]`
Lemmas referenced :  subtype_rel_self not_wf equal_wf uall_wf iff_wf and_wf isect_wf set_wf eu-point_wf eu-between-eq_wf eu-between_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 lemma_by_obid isectElimination universeEquality functionEquality equalityTransitivity equalitySymmetry lambdaEquality cumulativity hypothesisEquality because_Cache setEquality productEquality productElimination lambdaFormation dependent_set_memberEquality axiomEquality isect_memberEquality

Latex:
\mforall{}[e:EuclideanStructure].  \mforall{}[a,b:Point].  \mforall{}[c:\{c:Point|  \mneg{}Colinear(a;b;c)\}  ].  \mforall{}[p:\{p:Point|  a-p-c\}  ].
\mforall{}[q:\{q:Point|  b\_q\_c\}  ].
(eu-inner-pasch(e;a;b;c;p;q)  \mmember{}  Point)

Date html generated: 2016_05_18-AM-06_33_19
Last ObjectModification: 2015_12_28-AM-09_28_20

Theory : euclidean!geometry

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