Nuprl Lemma : eu-extend_wf

`∀[e:EuclideanStructure]. ∀[a:Point]. ∀[b:{b:Point| ¬(a = b ∈ Point)} ]. ∀[c,d:Point].  ((extend ab by cd) ∈ Point)`

Proof

Definitions occuring in Statement :  eu-extend: `(extend ab by cd)` eu-point: `Point` euclidean-structure: `EuclideanStructure` uall: `∀[x:A]. B[x]` not: `¬A` member: `t ∈ T` set: `{x:A| B[x]} ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` eu-extend: `(extend ab by cd)` 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]`
Lemmas referenced :  subtype_rel_self not_wf equal_wf uall_wf iff_wf and_wf isect_wf eu-point_wf set_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:Point].  \mforall{}[b:\{b:Point|  \mneg{}(a  =  b)\}  ].  \mforall{}[c,d:Point].
((extend  ab  by  cd)  \mmember{}  Point)

Date html generated: 2016_05_18-AM-06_33_16
Last ObjectModification: 2015_12_28-AM-09_28_38

Theory : euclidean!geometry

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